School Science Lessons
(UNPh28.1)
2024-07-25
Refraction of light Lens
Contents
28.1.1 Refraction
28.1.2 Birefringence, double refraction
28.1.3 Thick lens, refraction
28.1.4 Thin lens, refraction
28.1.1 Refraction
Abbe refractometer
28.4.0 Refraction of light
28.4.02 Laws of refraction, Snell's law
28.4.03 Real depth and apparent depth
28.4.01 Refractive index
28.190 Refractometers
Experiments
28.5.7 Acrylic / lead glass refraction
28.5.4 Coin in a cup, rising coin illusion
28.5.5 Light in a fish tank
28.4.6 Mirage illusion
28.11.3 Model refracting telescope
28.10.11 Optical instruments
28.121 Refraction in a smoke box
28.122 Refraction in water illusion
28.5.9 Refraction of light, air to water, in air
28.91 Refraction of waves in a ripple tank
28.125 Refractive index, Measure refractive index
28.4.07 Refractive index of ice
28.4.01 Refractive index, Snell's law, real depth and apparent depth
28.123 Refractive index using real depth and apparent depth
28.124 Refractive index using real depth and apparent depth, air to liquid
28.5.2 Refraction tank, ripple tank, aquarium
28.1.5 Refracting telescope, Galileo's telescope
28.88 Straight pulses in a ripple tank
28.4.2 Use same refractive index substances (Ghost crystals)
28.130 Water lens magnifier, water lens
28.1.2 Birefringence, double refraction
28.181 Birefringence, calcite crystals
28.189 Birefringent clear plastics
28.188 Birefringent mica
28.1.3 Thick lens, refraction
28.10.3 Barrel and pincushion distortion
28.10.2 Chromatic aberration
28.10.6 Lenses, water flask lens
28.1.4 Thin lens, refraction
Thin lens: convex lens (converging lens), concave lens (diverging lens)
28.8.01 Thin lenses, refraction
28.119 Focal length of a convex lens
28.2.06 Ray diagrams for lenses
Experiments
3.7 Burn with a magnifier (Primary)
28.8.4 Convex lens, concave lens, ripple tank
28.8.3 Concave lens, focal length of concave lens using lens formula
28.8.1 Convex lens forms an image
28.128 Image with a convex lens, magnifying glass
28.120 Light rays through lenses
28.129 Magnifying power of a lens
28.131 Optical bench for studying lenses
28.88 Straight pulses in a ripple tank
Make pulses by giving a cylindrical wooden rod a sharp push forward and back in the ripple tank.
This motion produces continuous waves.
The ripples are wider near the rod, but sharper as they move away.
The ripples are sharpest when the filament of the light bulb is parallel to them.
28.91 Refraction of waves in a ripple tank
Put a plate of glass in the middle of the ripple tank to create a sloping depth.
Note the distance between crests (wavelength) as the depth becomes more shallow.
The wavelength is less and the velocity of the wave is also lower in the shallow water than it is in the deep water.
28.119 Focal length of a convex lens
Focal length of a lens, 1 dioptre (UK), diopter (US) = 1 / focal length, in metres
Experiment
Attach a sheet of white paper on a wall opposite a bright window with the sun not visible, because it is behind an outside object, e.g. a tree.
The light rays passing through the window from the distant sun will be almost parallel.
Hold a convex lens vertically about 5 cm from the paper the move it in a straight line towards the window until a clear image of the window appears on the white paper at a distance of the focal length of the lens.
28.120 Light rays through lenses
See diagram 28.120: Ray diagrams for lenses.
Parallel rays of light that pass through a convex lens, converging lens, all pass through the principle focus, F.
Parallel rays of light that pass through a concave, diverging lens, diverge as if coming from the principle focus, F.
In the diagram, 1. to 4 are convex lenses that form real images when the object is more than one focal length from the lens.
Light rays come from a distant object,
The object is twice the focal length from the lens,
The object is between the focal length and twice the focal length from the lens,
The object is less than the focal length from the lens,
A concave always produces the same kind of image.
Experiment
Take the lenses from an old pair of spectacles or used optical instruments, or purchase reading glass lenses and hand magnifiers.
Cover the window of a smoke box with a piece of black cardboard with three holes punched in a vertical line.
The holes should be the same distance apart, but the distance between the two outside holes should be a little less than the diameter of the lens.
Arrange a torch supply parallel to light rays.
Fill the box with smoke and hold a double convex lens in the path of the three beams of light so that the middle beam strikes the centre of the lens.
Note the beams on the opposite side of the lens from the source of light.
Repeat the experiment using a double concave lens.
28.121 Refraction in a smoke box
See diagram 28.212: Refraction in a smoke box.
Refraction is the change in direction of light as it crosses a boundary from one optical medium, e.g. glass, into another medium, e.g. air.
Light bends towards the normal when entering a medium that is optically more dense.
Light bends away from the normal when entering an optically less dense medium.
Light paths are reversible for refraction.
The incident ray, refracted ray, and normal to the boundary at the point of incidence, all lie in the same plane.
Experiment
Fasten a piece of black cardboard with a single hole in it 8 mm square over the window of the smoke box.
Arrange a torch to shine a beam of light into the box.
Fill a large, preferably rectangular, bottle with water and add a few drops of milk or a pinch of starch or flour to make the water cloudy.
Cork the bottle.
Fill the box with smoke.
Hold the bottle at right angles to the beam of light and note the direction of the light through the water.
Tilt the bottle at different angles to the beam of light and note how the path of light through the bottle changes.
28.122 Refraction in water illusion
See diagram 28.122.3: Rising coin illusion.
See diagram 28.122.1: Depths in a swimming pool.
See diagram 9.122.2 : Bent stick illusion.
Experiments
1. Drop three stones (P1, P2, P3) in a flat bottom swimming pool.
Drop P1 below you, P2 farther away and P3 at the far side.
Look at the three stones from a position directly above P1.
Stone P1 appears to be at the greatest depth, P2 at lesser depth and P3 at still lesser depth.
The bottom of the swimming pool filled with water appears curved when viewed from above.
If the refractive index of water = 1.33, the apparent depth of the swimming pool looking straight down, normal view, = true depth / 1.33 = 3 /4 × true depth.
2. Place a stick in a tall container of water, so that part of the stick is above the surface.
Note where the stick enters the water.
The stick appears bent, because the light rays refract as they pass from water to air.
The image of each point on the stick below the water forms above its real position, because of refraction at the air / water interface.
3. Put a coin in a non-transparent, short and thick cup on the table. Stand away, and arrange your line of vision, so that you can just see a point A on the far side of the coin.
Your view of the coin is almost shut out by the wall of the cup.
Keep the position of your head unchanged while pouring water into the cup without moving the coin.
As you pour in the water, the coin appears to rise, so you can now see the entire coin.
The positions of A1 and B1 are the intersection of the backwards extensions of the refracted ray and the ray from A or B.
This ray is vertical to the surface of water and not refracted.
The refracted ray from A is parallel to the refracted ray from B.
4. More than half fill a tall transparent glass with water.
Insert a pencil so that the side of the pencil touches the right hand top of the glass and the lower end touches the left inner wall of the glass, but not the bottom.
Looking down into the water, see the lower end of the pencil touching the wall.
At the same time move your left finger from up and down along the wall of the glass
until you think the finger points to the lower end of the pencil.
Look through the side of the glass to see the actual position of the pencil.
It is under your left finger.
The position of the left finger is the position of the image of the end of the pencil.
28.123 Refractive index using real depth and apparent depth
See diagram 28.123: Real depth and apparent depth of glass.
Experiment
Place a block of glass on the table.
Place a pin close to the side of the glass at O.
The head of the pin may be seen from point A, at the edge of the glass opposite O.
Place an inverted drawing pin at B on the glass.
Adjust the position of B so that its point, coincides with the image of the pin at A seen through the glass.
Measure the lengths of OA and A2.
The plane CD with point A is the refraction plane of light, the refractive index from air into glass = AO / A2.
28.124 Refractive index using real depth and apparent depth, air to liquid
See diagram 28.124: Real depth and apparent depth of water.
Real depth and apparent depth of water is the curving of light around edge object and consequent spreading when it passes through a narrow gap.
A single slit diffraction pattern differs from double slit interference.
Experiments
1. Observe a vertical filament lamp slit formed by holding two finger together and looking through the narrow gap between the fingers.
2. Attach a pin at O to the bottom of a beaker with Plasticine (modelling clay).
Place the beaker on the white paper on the table.
Pour water into the beaker without disturbing the pin at O.
Look down to see the image I of the pin at O through the liquid surface.
Horizontally clamp another pin S to a stand near the beaker.
Adjust the stand to make S at the same height as I.
Mark the position of S on the outside of the beaker.
Pour off the water in the beaker without disturbing the pin at O.
Measure OL and IL, where L is a point on the surface of the water.
Repeat the experiment with different heights of water.
Calculate the reflective index from air into water = OL / IL.
28.125 Measure refractive index
See diagram 28.125.1: Refraction through glass block.
See diagram 28.125.2 : Refractive index.
Measure refractive index
Snell's law: sin i / sin r = n, a constant called the refractive index.
Substance and refractive index (for liquids at 20oC): diamond 2.4173, flint glass 1.655, crown glass 1.517, ethanol 1.361, water 1.33299, carbon dioxide 1.00450, air 1.000293 vacuum 1.0.
Experiments
1. Attach a black paper collar to the front of an electric torch.
Prepare a screen with a 1 cm diameter hole, or use a CD-ROM disc as a screen.
Hold the screen in front of the electric torch to limit the light beam to a narrow, horizontal beam.
Put a rectangular container, e.g. a fish tank or transparent plastic box, on a sheet of white paper on the table.
Draw a line on the white paper at right angles to the middle of the container, the normal.
Draw another line at 45o to the first line.
Fill the container with saltwater and add drops or milk or fluorescein.
Direct a beam of light along the 45o line into the container, the incident ray.
Note the path of the beam of light through the water.
Use smoke or chalk dust scattered in the air to make the beam of light visible in the air before entering and after leaving the container.
Look through the end of the container, looking along the ray, to see that it is straight.
The angle between the normal and the incident ray is the angle of incidence, i.
The angle between the normal and the path of the light beam through the water is the angle of refraction, r.
Refractive index = sin i / sin r.
The beam of light leaving the container, after passing through the water, is the emergent ray.
The incident ray and the emergent ray are parallel so there is lateral displacement between them.
Lateral displacement depends on the breadth of the container, the angle of incidence and the refractive index of the air and the solution in the container.
2. Repeat the experiment by putting a rectangular slab of glass, or a rectangular plastic box contained full of a transparent solution, on white paper on the table.
Draw the outline of the slab on the white paper.
Place a pin, X, at the middle of the nearest side of the slab.
Draw a line through X at 45o to the side of the slab.
Look along the line and put two pins, A and B, on the line and two pins, C and D, in line with A and B on the opposite side of the slab.
Put a pin, Y, where a line through DC meets the slab.
Remove the slab and draw the normal at X (X1 to X2) and the normal at Y (Y1 to Y2).
The path of the light ray is ABXYCD.
Use a protractor to measure the angle of incidence AXX1 and the angle of refraction X2XY.
Calculate the refractive index, sin AXX1 / sin X2XY.
Check that AXX1 = DYY1, and X2XY = Y2YX.
If refractive index of glass = 1.5, a glass slab viewed from the normal appears to be 1 / 1.5 = 2 / 3 of its true thickness.
3. Put a pin against the far face of a glass slab.
Hold a pointer down over the slab and move it until it is above the image of the pin, as seen through the slab.
If the true thickness of the slab = T, and the apparent thickness = AT, i.e. the distance of the pointer from the front of the slab, then refractive index = T / TA.
28.128 Image with a convex lens, magnifying glass
See diagram 28.217: Image with a convex lens.
Experiments
Darken all the windows in a room, but one.
Hold a convex lens (hand lens, magnifying glass) in the window and direct it at the scene outside.
Bring a piece of white paper slowly near the lens until the image picture forms.
Note the position of the image.
28.129 Magnifying power of a lens
Magnifying glass, glass lens, magnification × 3.75 mm diameter
Magnifying glass, bifocal, plastic lens, magnification 2 × and 6 ×3.75 mm diameter
Magnifying lens, hand lens, folded magnifier, magnification 10 ×
See diagram 28.218: Magnifying power of a lens.
Experiments
Use a magnifying glass to get a clear image of the lines in an exercise book.
Adjust the distance of the magnifying glass so that a line seen through the magnifying glass coincides with a line seen outside the magnifying glass.
Compare the number of spaces seen outside the lens with a single space seen through the lens.
The lens shown in the diagram magnifies three times.
Linear magnification is the ratio of the size (height) of the image to that of the object or the image distance to the object distance.
Magnification is the measure of enlargement or reduction of an object in an imaging optical system, e.g. X100.
In astronomy it is the factor by which an image produced by an optical device increases the angular size of an object.
Magnification of a telescope = focal length of the telescope / focal length of the eyepiece.
28.130 Water drop magnifier, lens
See diagram 28.1.17: Water lens.
Experiments
1. Roll the end of a copper wire around a thick nail to make a loop.
Cut the wire to leave a handle.
Dip the loop in water then take it out so that the water in the loop is the shape of a convex lens.
Look at the loop from the side to see the shape of the convex lens with the centre thicker than the edges.
Use the water lens to look at a line in the palm of your hand.
Move the lens towards and away from your hand to see the line become upright then inverted.
2. Very gently knock the loop so that the meniscus breaks then reforms to form a new water lens in the shape of a concave lens.
Look at the loop from the side to see the shape of the concave lens with the centre thinner than the edges.
Use the water lens to look at lines in the palm of your hand.
Move the lens backwards and forwards.
3. Put a drop of water on a piece of clean glass.
Observe the lines in the palm of your hand again.
The drop of water acts as a magnifier.
4. Use needle nose pliers to bend the end of a "slide on" paper clip to form a loop.
Dip the loop into a beaker of water then tap it against the side of the beaker to form a water lens inside the loop.
The water lens could be a convex lens (widest in the middle) or a concave lens (thinnest in the middle).
Examine the letter "e" with your water lens.
Note whether the lens is a convex lens or concave lens.
Dry the loop and try to make the other kind of lens.
28.131 Optical bench for studying lenses
See diagram 28.219: Optical bench for studying lenses.
An optical bench allows you to hold mirrors and lenses in position and to measure distances accurately with a metre scale.
Use wooden or plastic blocks with grooves that just fit over the metre scale.
Stick a pin into the centre of each block.
Use strips of tin screwed to the side of the blocks to make lens holders.
Attach a torch bulb to a block as a light source.
28.1.5 Refracting telescope, Galileo telescope
See diagram 36.65: Refracting telescope.
Experiment
Use two convex lenses, one with long focus and slightly thick diameter, another with short focus and slightly thin diameter.
Hold each lens opposite to some object afar.
Place a piece of white paper behind each lens to find the clearest image of the object on the paper.
Record the approximate value of each focus.
Use hard cardboard to roll two cylinders with nearly equal diameters and fix a lens on each cylinder.
The length of each cylinder 2-3 cm longer than the focus of its lens.
The fixing methods: use a piece of hard cardboard to roll two cylinders that can enclose their lenses; control the cylinders with thread or rubber tape.
Then glue the cracks on their insides and outsides with white adhesive plaster.
Glue a circle of hard cardboard strip at 0.5-1 cm from the rim of the slightly thick cylinder.
Place the long focus lens as the objective lens at left of the hardboard strip.
Then glue another circle of hard cardboard strip at the left of the lens so that the lens is fixed between two circles of hard cardboard strips.
Like this, fix the short focus lens at the slightly thin cylinder as the eyepiece.
At another end of the slightly thick cylinder cut a 3 mm × 1-2 cm quadrate window whose longer sides are horizontal
At the opposite side cut another same window, making sure that the focal plane of its lens is located at some axis section between the two windows.
Like this, cut two same windows with the above at another end of the slightly thin cylinder.
Insert the thin cylinder into another one and screw the thin one to make the two pairs of windows just opposite.
Separately insert two M3 screws through the inside of the cylinders and gently screw two nuts on the outside.
Let the objective lens face some object afar with then gently move the thin cylinder horizontally.
You may see a clear image of the object when the two focal planes coincide.
Here a contracted, inverted, real image of an object forms at the focal plane of the objective lens.
The real image forms an amplified virtual image infinite far from the eyepiece.
The amplification of this magnifying glass is the ratio of the focal length of the objective to that of the eyepiece.
:28.2.06 Ray diagrams for lenses
See diagram 28.120: Ray diagrams for lenses.
For the lens, the image forming properties depends on refraction through the lens material.
The focal length will depend both on geometric factors and the index of refraction of material of the lens.
28.4.0 Refraction of light
Light travels more slowly when it moves from a less dense medium to a more dense medium.
When the direction of the light is at right angles to the boundary, the wavelength decreases, but the frequency remains the same.
If light passes through air then glass, then the refractive index of the glass = speed of light through the air / speed of light through the glass.
So, refractive index must be < 1.
When the direction of the light is not at right to the boundary, the light changes speed and direction This is because the light that first meets the boundary slows before the light that later meets the boundary.
The change of speed and direction is called diffraction.
Deep and shallow water cause water waves to behave as if moving between two different media.
The side of the wave to first meet the shallow water slows before the rest of the wave.
Tsunamis occur when huge waves slowly and rapidly increase in height when entering shallow water.
Tourmaline (in Pegmatites), NaFe3Al6[(OH)4(BO3)3, Si6, O18], has double refraction.
28.4.01 Refractive index
See diagram 28.125.2: Refractive index, Refraction at flat surfaces.
Refraction is the change in direction of light as it crosses a boundary from one optical medium, e.g. glass, into another optical medium, e.g. as air.
Light bends towards the normal when entering a medium that is optically more dense, and away from the normal when entering an optically less dense medium.
Light paths are reversible for refraction.
28.4.02 Laws of refraction, Snell's law
The incident ray, refracted ray, and normal to the boundary at the point of incidence, all lie in the same plane.
Snell's law: sin i / sin r = refractive index, n.
Refractive index, n = sin i / sin r, where medium x is air and y is another medium (n >l).
Absolute refractive index of any medium is the ratio sin i / sin r for light passing from a vacuum into that medium.
Absolute refractive index of glass is from vacuum to glass or glass to vacuum.
Relative refractive index of glass is from air to glass or from glass to air.
28.4.03 Real depth and apparent depth
Speed of light in a medium changes with Snell's law.
So when looking from air into a more refractive medium, e.g. water, objects appear to be at a shallower depth.
Apparent depth in water = real depth × refractive index air / refractive index water.
28.4.07 Refractive index of ice
Freeze water by pumping in a hollow acrylic prism and measure the minimum deviation.
If refractive index of water = 1.333, then for ice is 1.309.
By using a semi-circular tank to hold the liquid you can avoid the refraction at one boundary.
Measuring critical angle rather than refraction angle avoids other problems.
This method is good for measuring the refractive index of ice, but getting a good piece of clear ice of the right shape is not easy.
28.4.2 Use same refractive index substances
See diagram 28.4.2: Cotton wool over methyl salicylate.
See 3.4.2.5.1: Ghost crystals, sodium polyacrylate, acrylic sodium salt polymer.
"Expanding Cubes", invisible in water (toy product)
Experiments
1. Place an eyedropper in a liquid using an index of refraction matched to the glass.
2. Use a small Pyrex beaker with graduations on the side or write words with a grease pen on the side.
Put the small beaker in a larger Pyrex beaker.
Pour an oil, e.g. Johnson's baby oil, Wesson oil, into the smaller beaker until it flows over into the larger beaker.
The part of the beaker below the surface of the oil almost disappears and the gradations or words seem to float on the oil.
The observations depend on the refractive index of the glass in the beaker being almost the same as the refractive index of the oil.
There is no reflection or change in refractive angle at a boundary between two transparent substances with the same refractive index.
3. Place a small Pyrex beaker inside a larger beaker.
Pour Johnson's baby oil or Wesson oil into the smaller beaker until the baby oil overflows into the larger beaker.
As the baby oil gradually rises inside the larger beaker the smaller beaker gradually disappears.
The baby oil has a refractive index equal in value to the refractive index of the Pyrex glass.
Close matching of the refractive indices make the smaller beaker practically invisible.
If the beaker has graduations or words they will appear to be floating in the liquid.
Many young students are fascinated by this experiment.
4. Wind white wool around a small heavy object, e.g. a coin, until you cannot see the object.
Drop the wrapped object into methyl salicylate solution.
As the wool absorbs the methyl salicylate it become transparent and you can see the object again.
5. Divide a large jar into two sections with a sieve of glass rods.
The upper section of the jar contains a wad of fluffy cotton wool.
The lower section of the beaker contains methyl salycilate liquid.
The cotton wool remains in place, because it has been stuffed into the jar and is pushing against the sides of the jar.
It remains dry, because it does not touch the methyl salicylate liquid below.
However, the cotton wool contains a secret coin hidden in the centre.
The coin cannot be seen, because the dry cotton wool is opaque.
Invert the jar so the methyl salicylate saturates the cotton wool.
The saturated cotton becomes transparent so the coin hidden in the centre of the cotton wool can be seen.
6. Use two microscope slides and cut a piece of Perspex with glass side walls made of slides, glued together with silicon, to make a mini tank.
It can be used to test refraction with different salt solutions, type of salt used and concentrations.
However, the changes are very small and you need precision equipment to measure them.
Use a spectroscope with a vernier gauge for measuring angle changes, down to 0.01 degree.
Measure of index of refraction of salt and sugar concentrations in water.
Measuring refractive index with temperature change is difficult, because the temperature of the solution changes too quickly.
So the observer cannot be certain of what the temperature was when the angle reading was taken.
7. If using glass jars and glass fish tanks it is difficult to get reliable data.
Ray boxes with white light seem to spread the beam too widely.
Laser pointers give a good beam across the base of a fish tank, but it is difficult to mark the exit point as the beam refracts leaving the tank.
28.4.6 Mirage illusion
A mirage is an optical illusion usually caused by refraction in heated air.
It may also appear as the reflected image in the sky of a distant object.
A mirage results from seeing through turbulent air For example, puddles of water may appear on an ascending hot road, a water lake may appear in the desert, heat shimmers over engines.
A mirage can be photographed, so it is not an optical delusion!
Experiments
1. Look at an object on the other side of a hot engine or a hot road.
The object will appear distorted, because the refractive indexes of warm and cold air are different.
This is one cause of mirages in the desert.
2. To create a mirage, direct the image from a slide projector just above a brass plate heated with a Bunsen burner.
28.5.1 Refraction through glass block
See diagram 28.125.1: Refraction through glass block.
Experiment
A single beam of light is used to show refraction through a rectangular block of glass.
28.5.2 Refraction tank, ripple tank, aquarium
25.3.1.0 Ripple tank, wave tank
Experiment
Rotate a beam of light in a tank of water containing some fluorescein.
28.5.3 Refraction model
Experiments
Roll an axle with independent wheels down an incline with one wheel on cloth the other on the plain board.
28.5.4 Coin in a cup, rising coin illusion
See diagram 28.122.3: Rising coin illusion.
Experiment
Pour water into a beaker until a coin at the bottom previously hidden by the side is visible.
28.5.5 Light in a fish tank
Experiment
Position a lamp in an opaque fish tank so that you cannot see the filament.
Add water to the fish tank until you can see the light from the filament over the edge of it.
28.5.7 Acrylic / lead glass refraction
Experiments
Hold a stick behind stacked lead glass and acrylic blocks.
The image of the stick is shifted when viewed off the normal to the surface of the blocks.
28.5.9 Refraction of light, air to water
See diagram 28.5.9: Refraction through milky water.
Experiments
1. Observe the reflection of a beam of light from air into water by adding drops of milk to water in a glass and stir it until the colour is uniform.
Put the glass of milky water in the sunlight.
Make a small hole in a piece of cardboard.
Hold the piece of cardboard so that a beam of sunlight hits the side of the glass below the level of the milky water.
Note the direction of the beam through the water.
Raise the piece of cardboard so that the beam of sunlight strikes the surface of the milky water.
Observe how the beam changes direction where it hits the water.
The beam is refracted.
Note that the angle between the surface of the milky water and the refracted beam depends on the angle between the water and in incoming, incident, beam.
To observe clearer, place another cardboard above the cup to shade the cup.
2. If sunlight is not strong, use a torch in a black box with a hole in the bottom to allow a beam of light to fall on the surface of the milky water > 90o.
The bending effect is more obvious if this experiment is done in a dark room.
If the angle of incidence is 90o no change in direction occurs.
3. Pour a few drops of milk into a glass of water to cloud the water.
Punch a small hole in a piece of dark paper or cardboard.
Place the glass in direct sunlight, and hold the card upright in front of the glass so that a beam of sunlight shines through the hole.
First hold the card so that the hole is just below the water level.
Note the direction of the beam in the water.
Then raise the card until the beam strikes the surface of the water.
Note the direction of the beam of light and experiment to find out how the angle at which the beam strikes the water affects the direction of the beam in the water.
28.8.01 Thin Lenses, convex lens (converging lens), concave lens (diverging lens)
See diagram 28.120: Ray diagrams for lenses.
See diagram 28.8.0: Convex lens, Concave lens, Make a diverging lens.
Lens formula: 1 / u + 1 / v = 1 / f
Magnification = height image / height object = v / u.
Projected Filament with thin lenses
Experiment
Turn on the light bulb.
Move the light bulb to focus the image on the side wall.
The focal lengths are marked on the lenses.
Show the effect of aperture size on the sharpness on the focus by placing different sized stops in front of the lens.
Concave lens (diverging lens)
Parallel light rays diverge as if coming from the principal focus.
Images are always virtual, upright, diminished, and less than one focal length from the lens.
The image formed by a diverging lens is virtual, erect, and diminished, and always lies on the same side of the lens as the object does.
The virtual image of an object is always closer to the lens than the object itself.
The image formed by a diverging lens is virtual, erect, and diminished, and always lies on the same side of the lens as the object.
The virtual image of an object is always closer to the lens than the object itself.
Convex lens (converging lens)
Parallel light rays converge through the principal focus.
Real image forms when object is more than one focal length from the lens.
Virtual image forms when object is less than one focal length from the lens.
Convex (converging) lenses are wider in the middle than at the edges.
Parallel light converges through a point called the principal focus, F.
Images in a convex (converging) lens: Real images form when an object is further than one focal length from the lens.
(1 / v - 1 / u = 1 / f), where u is the object distance from the lens, v is the image distance from the lens, f is the focal length of the lens.
Magnification = (Hi / Ho) = (f / So) = (Si / f = v / u), where Ho is the height of the object, Hi is the height of the image,
So = object distance from the principal focus, Si = image distance from the principal focus.
Virtual images form when the object is less than one focal length from the lens.
The types and positions of the image formed by a converging lens depend on u, v, f, and their relationship.
Image is a picture or appearance of a real object, formed by light that passes through a lens or is reflected from a mirror.
If rays of light actually pass through an image, it is called a real image.
A mirror forms an image by the law of reflection.
The focal length of a mirror depends only on geometrical considerations.
The properties of the material do not affect the focal length when light reflects from a mirror surface.
For the lens, the image forming properties depends on refraction through the lens material.
So the focal length will depend both on geometric factors and the index of refraction of material of the lens.
For both lenses and mirrors, the image and object distances are related by the same equation:
(u-1+ v-1 = f-1) or (1 / f = 1 / u + 1 / v),
where u is the distance from the object to the optical centre of the lens or to the mirror pole viz.
object distance, v is the distance from the image to the optical centre of the lens or to the mirror pole viz.
image distance, f is the focal length of the lens, which is positive for converging lenses and negative for diverging lenses.
The types and positions of the image formed by a converging lens depend on u, v, f, and their relationship.
See following table of the image formed by a converging lens and applications:
Table 28.8.0
Position
Number		 Position of object Position of image Description of image Application
1 u = infinity v = f Image on other side of lens Find focal length
2 infinity >u >2f f < v < 2f Real, inverted, diminished Eye, camera
3 u = 2f v = 2f Real, inverted, same size .
4 2f >u >f 2f < v < infinity Real, inverted, magnified Slide projector
microscope
5 u = f v = infinity No image Searchlight
6 f >u >0 v < 0 Virtual, upright, magnified, image on same side of lens Magnifying glass

28.8.1 Convex lens forms an image
See diagram 28.217: Image using a magnifying glass.
Lens formula and magnification, characteristics of images formed by thin lenses including a lens equation relating object distance.
, u, image distance, v, and focal length, f, and suitable conventions (1 / v + 1 / u = 1 / f), magnification.
M = (Hi / H0), ray diagrams to show image formation with thin lenses, combinations of lenses.
Experiment
Making the scene "shine" on a piece of paper.
Use a piece of paper to receive the real image formed by a convex lens.
Close the door of a room and cover its window just leave a light beam at the corner.
Hold a convex lens facing the scene outside window at the corner.
Move a piece of white paper parallel to the lens to close the lens slowly.
Observe the image on the paper and compare it with the practical scene.
28.8.3 Concave lens, focal length of concave lens using lens formula
See diagram 28.8.3: Focal length of concave lens.
Concave (diverging) lenses are narrower in the middle than at the edges.
Parallel light diverges as if coming from a point called the principal focus, F.
Experiment
Insert the pin into the stand to fix the pin.
Place the needle shaped object O in front of the concave lens.
The pin as a searcher S searches the position at which S coincides with the object's image I between O and lens L.
Here you may see both I and S through L's upper part.
Adjust the position of S to decrease the optical parallax between S's visible part and I.
Measure the object distance u and the image distance v.
Repeat the experiment with different u 4 times.
Calculate the focal length of the concave lens with following formula: (1 / v + 1 / u = 1 / f).
28.8.4 Convex lens, concave lens, ripple tank
25.3.1.0 Ripple tank, wave tank
Experiments
1. Refraction due to depth differences over a lens shaped area in the ripple tank.
2. Trace rays with lenses.
Examine parallel rays passing through a lens element and converging.
3. Project the filament of a lamp using a thin lens on the wall.
4. Form real images with a source and screen at the ends of a long optical bench and show how the two positions a lens will produce an image.
5. Use an illuminated arrow using a converging lens to project an image on a screen.
6. Try to project an image using a thin concave lens.
7. Find the focal length of a lens then find the focal length of the same lens in water.
8. Project pinholes with a lens.
Prick pinholes in a black paper covering a long filament bulb.
Bring the multiple images into one image using a converging lens.
Connect a microwave lens and prisms of stacks of properly contoured aluminium sheets separated by just over one half the wavelength microwave lens.
9. For a fish-eye view, fill a pinhole camera with water or solid Lucite, (Perspex).
10. Show the effect of stopping down a lens and depth of focus.
Use a 12 cm long glowing wire as an extended object.
28.10.2 Chromatic aberration
Fringes of colour about an image are caused by a lens with different refractive index for different wavelengths.
The different wavelengths focus at different distances from the lens and with different magnification.
The problem occurs in colour photography and is solved with special lenses or special combinations of lenses.
A diaphragm moved near the focus selects red or blue light from beams passing through the edge of a lens.
Project spots of light on a screen from several points on a lens.
28.10.3 Barrel and pincushion distortion
Experiments
Project an illuminated wire mesh using a large lens.
Place a diaphragm between the lens and the mesh for barrel distortion and between the lens and the screen for pincushion distortion.
28.10.6 Lenses, water flask lens
See diagram 28.212: Water flask lens.
Experiments
1. Direct a beam of light through a round flask filled with water.
2. Make fillable air lenses using convex and concave lenses filled with water and air.
3. See the effect of a spherical lens by comparing a thermometer at the centre of a water filled flask to a thermometer at the far side.
4. Make a wine bottle lens by filling a round flask using a wine bottle arch-shaped bottom inverted with water and fluorescein to show diverging light.
5. Make a watch glass lens, by forming a vertical lens by pouring various liquids into a watch glass.
28.10.11 Optical instruments
See diagram 28.10.11: Lenses and apertures.
Experiment
Turn on the light bulb.
Move the light bulb to focus the image on the side wall.
The focal lengths are marked on the lenses.
Show the effect of aperture size on the sharpness on the focus by placing different sized stops in front of the lens.
28.11.3 Model refracting telescope
Experiment
Arrange a long focus lens on the end of an optical bench pointing at an object through the window.
Bring a piece of white cardboard up on the opposite side of the lens to the place where the sharpest image of the scene is formed.
Bring a short focus lens up behind the cardboard until the cardboard is a little nearer the lens than its focal length.
Remove the cardboard and look through the two lenses at the object.
28.181 Birefringence, calcite crystals
See diagram 27.6.4.1: Model of calcite crystal lattice structure.
Calcite, calcium carbonate, CaCO3, is a naturally occurring birefringent crystal.
Along the optical axis each carbonate group forms a triangular cluster perpendicular to this axis.
The large birefringence of calcite is caused by the carbonate groups in planes normal to the optic axis.
It is used in the Nichol prism.
Experiment
1. Turn the crystal in the light and note the flashing surfaces.
Place a clear crystal, place it on a line and observe the refracted double line.
Calcite is an anisotropic crystal with two indices of refraction, 1.49 and 1.66, to produce a double refraction effect, a double image caused by light polarization.
Assemble a projector with the object stage containing calcite with a fixed pinhole stop.
The lens forms a double image of the pinhole stop on the projector screen caused by the birefringence of the calcite.
Rotate the object stage and observe one image remaining stationary, while the second image rotates around the first image.
2. Examine birefringence of a Plexiglas rod directly with a linearly polarized laser.
3. For pendulum model birefringence, strike a pendulum with a blow then wait 1 / 4, or 3 / 4 period and strike another equal blow at right angles to the first.
4. For double refraction model birefringence, a double pendulum displaced in an oblique direction will move in a curved orbit.
5. For Nichol prism birefringence, one of a pair of Nichol prisms is rotated as a beam of light from an arc lamp is projected through the Nichol prism.
6. For crystal structure of ice birefringence, place a thin slab of ice between crossed Polaroids.
28.188 Birefringent mica
See diagram 27.6.4.8: Colours in mica (University of Melbourne).
Birefringence is having a different refractive index for light in different directions.
Experiments
1. Rotate a mica sheet between crossed Polaroids.
2. Mica is birefringent.
The cleavage planes are such that an incident wave is split into two waves polarized vertically to each other.
On emergence from the crystal, the waves display a phase difference dependent on the thickness of the plate and the wavelength.
These two phase displaced waves interfere with each other to produce the interference colours displayed.
3. Examine mica interference by reflection of filtered mercury light from a mica sheet onto a screen.
Reflect light from a mercury point source off a thin sheet of mica onto the opposite wall.
28.189 Birefringent clear plastics
Birefringent clear plastics, polyethylene terephthalate (PET)
OrganicModels">Models, organic, PET, (Commercial).
Grilen polymer, fibre from polyethylene terephthalate Polyethylene terephthalate (PET), Dacron, soft drink bottle, Ethylene phthalate (C10H8O4), 192.17 g/mol
Birefringence is having a different refractive index for light in different directions.
Doubly refraction material includes the following:
1. A crispy transparent cellophane wrapping for confectionery, potato chips and computer disk packets.
2. Clear polystyrene rectangle from a window envelope.
Polyethylene terephthalate (PET), is transparent, high impact strength, impervious to acid and atmospheric gases, not subject to stretching.
PET is used for light-weight, shatter proof soda-pop and water bottles, peanut butter jars, cooking oil bottles, oven-ready meat trays, microwaveable meat trays.
Fibres from polyethylene terephthalate include "Melinex", Terlenka, Terylene, Trevira.
The 2-litre drink bottles used to have a second black polyethylene as a cup on the bottom for a strong base, but now have a bottom with five convolutions.
PET is a birefringent 2-dimensional orientated plastic.
See 3.5.3, Plastics recycling code, Polyethylene terephthalate, 1 PETE,
PET bottles can be colour sorted, ground into pieces and washed to sink, while caps and labels float off.
PET pellets can be recycled as bottles and fibres, e.g. carpets
Experiment
Place a square cut from doubly refraction material between fixed and rotatable Polaroid sheets crossed so that transmitted light is extinguished.
The 3 materials together let light pass through again!
PET bottles used to have a second black polyethylene as a cup on the bottom for a strong base, but now have a bottom with five convolutions.
PET is a birefringent 2-dimensional orientated plastic.
A birefringent material has a different refractive index in the two dimensions.
When polarized light passes through, this differential results in a rotation of the plane of polarization.
So crossed Polaroids are no longer crossed when material in between has caused a rotation.
The amount of rotation depends on the degree of orientation of the polymer molecules and thickness of the film.
28.190 Refractometers
Refractometers YHequipment, testing brix, (Commercial).
Refractometers are instruments to measure substances dissolved in water and certain oils.
Refractometers are used to determine the amount of dissolved solids in liquids by passing light through a sample and showing the refracted angle on a scale.
The scale most commonly used is referred to as the Brix scale.
The Brix scale is defined as: the number of grams of pure cane sugar dissolved in 100 grams of pure water (grams sugar/100 grams H20).
Other scales have been developed to measure salt, serum proteins (albumen) and urine specific gravity.
Sugar Refractometer 0 ~ 32%, Used to test the sugar content of fruit, fruit juices, wine, milk, soft drinks and yeast cultures.