By shining light from a hand-held laser through a rectangular plastic container filled with water we observe for several incident angles the change in the angle of the path of the beam on entering and leaving the fluid medium.  We also observe the angle of total internal reflection. 

Note:  Any glass or plastic container through which you can maintain a laser beam can be used for this experiment.  A rectangular container is preferable.  Where the instructions refer to a cassette case, use this container.

Trace the paths of rays into, through and out of opposite sides of the water-filled container.

• The liquid should transmit the light but should show you the path of the beam as well.

• Place the case on a sheet of paper and mark the paper as accurately is possible to reveal the directions and locations of the edges of the case (be sure you report the clever things you did to accurately mark the positions of the edges of the case).

• Shine the light so that it starts about 10 cm from the case, then strikes the case at an angle of approximately 45 degrees with the normal (i.e., the perpendicular) direction to the edge of the case.
• The light should continue through the case until it strikes the opposite side, and should then exit the case in a reasonably coherent beam. You should be able to see clearly where the beam enters and leaves the case.
• Make marks on the paper indicating where the center of the beam leaves the pointer, where it enters the case, where it leaves the case, and its position approximately 10 cm after leaving the case.
• When you report this experiment, be sure to specify how you managed to locate these points as accurately as possible.
• Take a lesson from one of the videotapes and clearly label these points so as not to get them mixed up with other points and reach absurd conclusions, (e.g., that the water has changed to a solid diamond).

• Repeat for angles of 15, 30, 60 and 75 degrees from the normal direction.

Trace the paths of rays into, through and out of adjacent sides of the water-filled cassette case.

• Repeat the procedure, using angles of 15, 30, 45, 60 and 75 degrees, for rays that enter the long side of the cassette case and exit one of the short sides.
• Find and mark the path of the greatest angle for which the beam enters the long side but, due to its being totally reflected, fails to coherently exit the short side.

• Mark the path at the points where this beam originates, where it strikes the long side of the case, where it is reflected from the short side, where it exits the opposite long side, and at its position approximately 10 cm after exiting the long side.

Analyze the various paths

For each ray entering or exiting the cassette case, sketch the path of the ray and sketch the normal line (i.e., the line perpendicular to the case passing through the point where the ray strikes the case) and determine the angle of the incoming and the transmitted ray with the normal line.

• You may use a protractor, provided you use it correctly and read it correctly. Or you may use right triangles, as indicated in video clips, provided you construct the triangles accurately and measure them very carefully.

Using each ray through the long sides of the cassette case, obtain a value for the index of refraction of the water, using Snell's Law: sin(`theta1) / sin(`theta2) = n2 / n1. You may assume that the index of refraction of air is 1.

• Which of your values would you expect to be the most accurate and why?
• How well do your values compare with the accepted value for the index of refraction of water, which is approximately 1.34?
• Do you obtain the most accurate values for the rays you expected to yield the best results?

For each ray passing through the adjacent sides of the cassette case, determine the net change in the direction of the beam, from the original beam to the beam that exits the short side of the case.

• Graph the change in direction vs. the original angle with normal.
• Graph the final direction of the beam vs. the original angle with normal.
• From this graph estimate the original angle for which the final angle will be parallel to the short side of the container.

• Compare this with the original angle of the beam which reflected from the inner wall of the container rather than being transmitted.
• How should these angles be related and why?

Using a hand-held laser and a circular mirror cut from a soft-drink can we observe the focal point at which parallel rays incident on the mirror converge.  We also observe the paths of rays through circular lenses and the focal points of the lenses.   The lenses have been constructed from broken pieces of clear Christmas tree ornaments mounted on clear cassette cases and filled with water.

Trace the paths of parallel rays reflected from a circular mirror

Using any reasonably sharp steel knife (it should not damage a tempered steel knife to cut aluminum, but just in case don't use your best cutlery), cut a section like the one shown on the videotape from a soft drink can.

Determine the radius of the can.

• Using this radius with either a compass or a pencil and a piece of string, sketch a segment of a circle with this radius to match the section cut from the can.
• Be sure to clearly mark the center of the circle you used to sketch this segment.
• Sketch the segment on a piece of lined notebook paper and position the segment so that when the piece of the can is positioned on the segment you will be able to direct parallel rays toward it as indicated on the video clip.

Position the section on the paper, and if necessary adjust it as necessary so that its curvature matches that of the circular segment you sketched.

• Direct four beams at the section of the can (hereafter referred to as the mirror) and trace their paths toward and away from the mirror.

• The first beam should be a central beam, which is reflected from the mirror along the same path with which it approached the mirror.
• The second beam should be parallel to the central beam and approximately 1/8 of the container's radius to the right of the central beam.
• The third beam should be parallel to the central beam and approximately 2/8 (i.e., 1/4) of the container's radius to the left of the central beam.
• The fourth beam should be parallel to the central beam and approximately 3/8 of the container's radius to the right of the central beam.

• Mark the center of each beam as it leaves the pointer at a distance of about 15 cm from the mirror, at the point where it strikes the mirror, and at the most distant point you can reasonably locate after the beam is reflected from the mirror.

Trace the paths of parallel rays entering a circular container full of liquid (a circular lens).

Using similar techniques to those used above, using a lined piece of paper (e.g., ruled notebook paper) to ensure that the beams are parallel, trace the paths of four beams through a transparent circular container filled with colored water or lightly colored soft drink, as specified below.

• The container should have a section with smooth sides and a very circular cross-section (i.e., that section should make a nice uniform circular cylinder),  and should have the approximate diameter of a soft drink container (20 oz. or larger--the larger the container the better your accuracy will be).  Many glass jars, soft-drink bottles, etc. make good containers for this experiment.  A petri dish might have been included with your kit and if so you may use it or any container of the above description.
• At and near the points where the beams will enter and leave the container, the container should form a smooth, uniform vertical cylinder.

By placing a 'screen' (e.g., the cassette case with the copy of the ruler taped to it) at the appropriate position behind the circular lens used in the preceding procedure, determine the distance at which the emerging beam appears to remain stationary as the laser is moved back and forth in front of the lens.

• Take care to keep the laser pointed in a consistent direction so that the beams striking the lens are all parallel.
• Observe how the dot on the screen will move in the opposite direction to your movement of the laser when the screen is far from the lens, and how it will move in the same direction when close to the lens.
• The distance at which the dot on the screen remains stationary will be the point at which the direction of movement of the dot changes.
• Mark this distance on your paper.

Analyze the various paths

Sketch the paths of the four beams to and from the mirror.

For the mirror, determine whether the angle of each incoming beam with the normal to the mirror is the same as that of the reflected beam.

• At each point where the beam strikes the mirror, sketch a radial line segment (i.e., a straight line segment from the center of the circle to the point).
• Sketch at each point a short line segment tangent to the mirror (the tangent will be perpendicular to the radial line segment).
• The radial line segment is perpendicular, or normal, to the mirror at each point.
• Determine the angle between the incoming beam and the normal, and between the reflected beam and the normal.
• Determine whether these two angles are equal.

For the mirror, determine as accurately as possible the point at which the reflected rays converge.

• The rays closest to the central ray of a truly circular mirror will converge almost perfectly; those furthest from the central ray will converge less perfectly.
• Determine the ratio between the point of convergence and the radius of the circle.

For the circular lens, sketch the paths of of the four rays and determine whether the path of the fourth ray is consistent with Snell's Law.

Sketch the paths of the four rays.

• For each ray, sketch the normal line as the ray enters and as it leaves the circle, and sketch the tangent line to the circle at each of these points.

• For a point on a circle, the normal line is a radial line from the center; the tangent line at this point is perpendicular to the normal line.

• Determine whether each ray is in fact deflected toward the normal as it moves from a lower to a higher index of refraction, and away from the normal as it moves may higher to the lower index of refraction.
• For the fourth ray, determine as accurately as possible the angle with normal before and after the ray enters the circle, and before and after it leaves the circle.
• Determine whether these angles are consistent with an index of refraction of 1.34 for water, 1.00 for air.

For the circular lens, determine the distance of the focal point from the lens.

Determine as accurately as possible where the four rays converge.

• The four rays should converge at a point 'behind' the lens. Determine the distance behind the lens at which the rays converge.
• Determine the ratio between this distance and the radius of the circle.

Note:  Due to the breakability of the original lenses this experiment has been modified to use a pair of thin plastic lenses.  Click here for the instructions for the modified experiment.

Using lenses constructed from broken pieces of clear Christmas ornaments we determine focal points and focal lengths of two concave and two convex lenses.

You will receive four lenses mounted on cassette cases. When the cases are placed in an upright position on a table, the lenses can be filled with any clear liquid. Water is recommended for most experiments.

The lenses are marked according to the diameter of the sphere from which they were broken. These diameters are either 3 inches or 4 inches (corresponding to about 7.6 cm or 10.2 cm).

The lenses are either concave (curving back in toward the cassette case) or convex (bulging out from the case).

On each lens are two small black dots, which will be used in one method of determining the focal points of your lenses.  If your setup does not have the two dots, place two small dots on each lens, with one dot about 2 mm above the center and the other 2 mm below the center (maybe 3 mm for the larger lenses).  You will end up with a top and a bottom dot, separated by about 4-6 mm.

We begin by determining the focal length of each of the convex lenses.

• First estimate the focal length of each lens by placing the screen 'behind' the lens and moving the laser back in forth in front of the lens, as you did with the circular lens in the preceding experiment.

• The focal distance is the screen distance at which, if you manage to keep the direction of the pointer consistent, the dot on the screen remains stationary.
• Measure the distance of this point behind the lens.

• Now determine the focal distance using the two dots on each lens.

• Place the screen at about twice the distance behind the lens as your estimated focal point; measure and note this distance.
• Using the line level to keep the laser pointer horizontal, direct the beam through the top dot on the lens and onto the ruler on the screen; note as accurately as possible the vertical position of the beam on the ruler.
• Repeat for the bottom dot.
• Measure the vertical distance between the dots, then using this distance and other observed distances construct an accurate picture of the paths of the beams.
• From your picture determine the distance from the lens at which the beams cross.
• This distance should be the focal distance.

• To check the focal distance, place the screen at this focal distance.

• Determine whether horizontal rays through the two dots on the lens strike the screen at the same vertical position.
• If this is the case, as it should be, then you have determined the focal distance.

• You should double-check the focal length at night by aiming you car so that the lights shine ahead for some distance, turning on the lights, and walking to a point about 100 feet in the beam of the lights.

• If you place the lens in the path of the beam, and move the screen back and forth behind the lens, at a certain distance the images of the car lights will focus down to two concentrated points. This distance should be the focal distance and should be identical to that determined by your experiment.

• You can also determine the focal distance on a sunny day by forming a concentrated image of the sun on your screen.

• The image of the sun should effectively shrink to a point at the focal distance.
• Do not attempt to look at the sun through this lens. If your eye is anywhere near the focal point, you will burn out parts of your retina and see dark blotches for the rest of your life.
• Don't leave the point image of the sun on the screen for long or you will burn a hole in the paper.
• Resist the temptation to start fires or to focus the sun on ants.

• Look through the lens at your finger.

• Move your finger close to the lens, then further from the lens. Note and describe what you see.
• What does the image of your finger look like when your finger is at the focal distance?
• What happens to the image of your finger if you move back and forth across the focal point?

Next determine the focal points of your convex lens.

• Observe first how there is no point at which the screen can be placed in order to keep the dot still as you move the pointer back and forth in front of the lens.
• Observe also that the further the screen is placed behind the lens, the larger the dot appears in the more it moves as you move the pointer.

Note:  Due to the breakability of the original lenses this experiment has been modified to use a pair of thin plastic lenses.  Click here for the instructions for the modified experiment.

Using the lenses from previous expreiments we investigate image formation, image size and object size.  Results are analyzed using the lens equation.

For this experiment you will need two small but fairly intense sources of light. The candles included in your kit would work very well.  As an alternative you can use two flashlights if you mask the lens of each so that only a circle in the center of about the radius of the bulb remains.  The candles are probably much more convenient.

You will also need a dark room and a flat surface such as a tabletop.

In this experiment you will use your convex lenses to

• create images of your light source, with the light source at various distances from your lens
• create images of other objects
• explore the relationship among image distance, object distance, focal length and magnification
• make a spotlight.

Create images of a single light source

You will use both convex lenses.  If you have not already done so, determine the focal length of both lenses by the most expedient method possible (recommendation:   form a sharp image of a distant candle and measure the focal distance directly).  

Begin by lighting one candle and placing it on a tabletop, or by turning on a flashlight and placing it on a tabletop aimed at the 4-inch lens.

Position the light source at the far end of the tabletop, at least 1 meter away from the other end (if your tabletop is too small, you might need to support the source on something at the same height as the tabletop).

About 20 cm from the other end of the tabletop, place the lens so it is facing the light source.

Place the screen behind the lens at the edge of the tabletop (about 20 cm from the lens), so that light shines from the source through the lens and onto the screen.

If the lights in the room are on, turn them off.

• Move the screen toward the lens until the image of your light source becomes as sharp as possible.
• Determine the distance from the center of the lens to the screen, and the distance of your light source from the center of the lens.
• Now move the light source to a distance of about 50 cm from the lens, locate the screen to form the sharpest possible image, and repeat your measurements.

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Repeat for distances of 40, 30 and 20 cm from the lens. For some of these measurements it might be necessary to change the position of your lens (it might be too close to the tabletop).

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Create images of a double light source

Light both candles and place them side by side.

Place the lens about 50 cm away from the two candles. The line from the candles to the lens should be perpendicular to the line connecting the two flames, so that has seen from the lens one candle lies a few centimeters to the right and the other a few centimeters to the left.

• Position the screen to form a sharp image of the two flames.
• Measure the distance from the candles to the center of the lens and from the center of the lens to the image.
• Measure the separation of the two flames, and the separation of their images.
• If you place something in front of the candle on the left, which image should disappear, the one on the left or the one on the right?  Why?

Report your observations:

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Repeat for distances of 30 and 20 cm. If the images get too far apart, you might have to form one image at a time on the screen.

Report your observations:

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Now move the candles to within 3 cm of the focal distance and repeat.

Repeat for distance of 1 cm outside the focal distance.

Report your observations:

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Make a spotlight

Place your lens on the tabletop at least 2 meters from a wall, with the wall behind the lens.

Place your source at a distance in front of the lens equal to the focal distance of the lens.

Look at the image formed on the wall. It should have the same shape and size as the lens, and should be sharply defined.

If this is not so, adjust the position of the lens so that it becomes so.

• Accurately measure the distance from the source to the center of the lens.

Report your observations:

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If you have a larger darkened area available, see how sharply you can make the image of the lens at a distance of several meters from a wall.

• Do the sharpness and the size of the sharpest image change with distance?

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Create an image

Now you will create an image of another object.

Select an object not more than a few inches high and not less than an inch high, and with a significant amount of white in its background. As an alternative, you could make a cone about 3 inches high out of aluminum foil use it as your object.

Place this object on the tabletop about 40 cm in front of your 4-inch lens.

Use your light source and the 3-inch lens as a spotlight to illuminate the object as brightly as possible.

• Place the screen behind the first lens and determine the distance of the object from the center of the lens, and the distance from the center of the lens at which the sharpest image of your object appears.
• Measure the height of the object and of its image.

Report your observations:

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Repeat for the same object a distance of 30 cm in front of this lens.

Report your observations:

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Analyze your results

If image distance is i, object distance is o and focal distance is f, then 1/f = 1/i + 1/o.

• Verify this formula for the image and object distances observed in each part of this experiment.

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If image distance is i and object distances o, then the magnitude of the magnification is the ratio i / o; this ratio is equal to the magnitude of the ratio of image size to object size.

• Verify this formula for the image an object sizes and distances obtained for the object in the last part of this experiment.

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For the two-candle images, verify that the distances between the images of the flames are in the same proportion to the actual distance as the image distance i to the object distance o.

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What is the evidence that the images of the two candles are inverted?

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Using a hand-held laser pointer and a diffraction grating consisting of lines on a rectangular transparency, we observe the maxima created when the light is directed through the pattern at various separations, and with various incident angles.  We determine the angular separation of the maxima and use this separation to estimate the wavelength of the light.  We then use sets of parallel straight lines on the same transparency to determine the wavelength of the light.

Stapled to the paper rulers in your lab materials package is a rectangular transparency a few inches on a side.   The transparency contains copies of various patterns of lines.

In at least one pattern the lines form a V.

• Orient the pattern so that the V is upright, with the widest spacing at the top.
• Move at least 3 and preferably 5 or more meters from a smooth wall.  Shine the laser through the V near the top of the pattern and observe the image made by the light on the wall.  Measure the distance from the transparency to the wall.
• Gradually move the laser down through the V, so that it shines between lines that move progressively closer and closer together. Observe what happens to the pattern on the wall.

• Continue moving down the V until you obtain the most distinct possible set of bright spots on the wall.
• Note the vertical position of the beam on the V.
• As best you can, determine for this position the average distance between the distinct bright spots formed on the wall.
• Measure the width of the V at this point, and the number of spaces between the threads across the width.
• Record also the distance to the wall.

There are also a few rectangular patterns consisting of parallel lines.  The spacing of the lines varies from rectangle to rectangle.

• Repeat the preceding exercise using different rectangular grids.
• For each grid determine the average distance between the bright spots on the wall, the average distance between the grid lines and the distance from the plastic rectangle to the wall.

According to your results, how is the spacing between the bright spots on the wall related to the distance between the lines?

What is the ratio of the spacing between the dots to the distance between the plastic rectangle and the wall?

What distance is in the same ratio with the spacing between the lines?