Refraction of Light by Glass

And Converging and Diverging Lenses©98

Experiment 12

Objective:To determine the law of refraction of light by glass using geometric ray-tracing; to become familiar with the characteristics of converging and diverging lenses.

DISCUSSION:

When a ray of light in the air strikes the surface of a transparent medium, such as glass at some angle θ1 to the normal of a surface, that part of the ray which passes into the glass is bent or refracted so that it leaves the surface at some other angle θ2. The situation is shown in Figure 1.

The ancients were aware of these phenomena and found that it was roughly true that

(1)

where k is a constant peculiar to the medium the light enters from the air. However, a better law (discovered in the early 17th century by Willebord Snell) is that

(2)

where n1 is a constant peculiar to medium 1 and is known as the index of refraction of medium 1 relative to medium 2. Similarly, n2, is the index of refraction of medium 2 relative to medium 1. When a ray of refracted light enters the eye, the observer interprets the ray as having traveled along a straight line from its source. The direction of this line is the direction at which light enters the eye. Consider Figure 2. Medium 2 is a rectangular glass plate, and medium 1 is air. Pins are placed at P1and P2. The observer views these pins through the glass, and then places a third pin at P3so that, when seen through the glass, the 3 pins are aligned. Actually the line of light connecting P1, P2and P3is bent at the first and second surfaces of the glass. These positions P1, P2and P3, along with the normal to the first surface, enable one to measure the angles θ1 and θ2.

If n2n1, the beam of light is bent toward the normal at the first surface in Figure 2. However if n2n1, the beam of light is bent away from the normal, as shown at the second surface. Since the sine of an angle cannot exceed unity, if n1sin θ1 > n2, the ray cannot be refracted. But the ray also cannot be absorbed by the surface, and so it is reflected back into medium 2.

When light passes through a prism, it follows a path dictated by the laws of refraction. Figure 3 shows light passing through a prism without reflection at a surface. Figure 4 shows internal reflection.


Note: The index of refraction of a medium with respect to air is commonly called n. Since nairis about 1.0003, the common measure of n will indicate the index of refraction of a give material with respect to air, instead of a vacuum.

A converging lens is a piece of transparent optics, usually glass or plastic, that causes parallel rays of light to converge or concentrate along the central axis of the lens. For example, a simple converging lens can concentrate enough sunlight (striking the Earth as parallel rays) to start a fire on a dry sheet of paper. In contrast, a diverging lens causes parallel rays of light to diverge or spread away from the central axis of the lens. For example, a simple diverging lens would spread out sunlight that went through it as though the sunlight were coming from a point along the central axis in front of the lens.

The optical axis of a lens is a line through the center of the lens and perpendicular to the plane of the lens. The focal point of the converging lens is that point on the optical axis at which rays of light from an infinitely remote source on the optical axis seems to diverge. It is also the point from which the rays of light that enter the lens parallel to the optical axis seems to diverge after passing through the lens.


The rules for constructing the image of an object are as follows:

  1. From a point on the object lying off the optical axis, draw a straight line to the lens, parallel to the optical axis, as shown in Figures 5&6. Change the direction of this line on the other side of the lens so that it:
  2. passes through the focal point, if the lens is converging
  3. seems to originate from the focal point, if the lens is diverging.
  1. From the same point on the object, draw a second straight line through the center of the lens, continuing it on the other side of the lens with its direction unchanged.
  1. If the extensions of the two lines constructed above converge after passing through the lens, draw the real image of the object- point at the intersection of the two lines. Or if the extensions of the two lines diverge, draw the virtual image of the object – point at the point from which the extended lines seem to diverge.

The images formed by the diverging lenses are always virtual because the transmitted rays of light always diverge. But the images formed by converging lenses may be real or virtual. They are real if the object is farther from the lens than is the focal point, and they are virtual if the object is nearer the lens than is the focal point.

It can be shown from the geometry of the rays in Figures 5&6 that in general

(3)

where so isthe distance of the object from the lens, si is the distance of the image, and f is the distance of the focal point from the lens. The following sign conventions are universally followed by optical scientists;

  1. The focal length f is positive for converging lenses and negative for diverging lenses.
  2. The object distance so, is positive when the object is on the incoming side of the lens, negative otherwise.
  3. The image distance si, is positive when the image is on the outgoing side of the lens, negative otherwise.

If two lenses are used in combination and are placed next to one another, the image that would be produced by the first lens acting alone becomes the object for the second lens. In this case, the effective focal length of f of the combination is given by;

(4)

where f1 and f2are the focal lengths of the separate lenses.

EXERCISES FOR PRISMS:

  1. Using the pins as objects, trace several independent rays of light through the rectangular prism. Suggested angles of θ1 are 5˚, 10˚, 15˚, 20˚, 30˚, and 70˚. Report this data in the form of a table with column headings of ray#, θincident , θrefracted , the sines of the angles, etc.
  1. For each ray of light, determine the index of refraction. Snell’s law states that this index is a constant. To what degree does your data support Snell’s Law?
  1. Setting the index for air to unity, is n2, the index for a glass constant? Determine the percent deviation of each determination of n2 from the average value, and also report the standard deviation.

EXERCISES FOR LENSES:

  1. Measure focal length of lenses marked red and green using object outside window.
  2. Place screen on end of optical bench opposite the window.
  3. Place one lens holder on optical bench and insert lens.
  4. Move lens back and forth on optical bench until you have the best image of a distant object.
  5. Lock the lens in place then measure and record the distance between the lens and the screen. This is the focal length of the lens.
  6. Repeat for remaining lens.
  1. Confirm Equation (3) for both lenses.
  2. Add the light source to the optical bench on the opposite end from the screen.
  3. Measure and record the image distance, si.
  4. Measure and record the object distance, so.
  5. Calculate f and compare to the f measured previously.
  6. Repeat for remaining lens.
  1. Using so and si found above and the calculated f, draw a to-scale ray diagram for each lens (in cm!).
  1. Build a simple telescope.
  2. Remove the screen and light source from the optical bench.
  3. Add a second lens holder.
  4. Put the longer focal length lens in the lens holder closer to the window. This is the objective of the telescope.
  5. Put the shorter focal length lens in the other holder. This lens is the eyepiece.
  6. While keeping the objective lens stationary, move the eyepiece until you can see a clear image through the two lenses. (note: the eyepiece should not be right against your eye.)
  7. Measure and record the distance between the two lenses.
  8. Calculate the magnification of your telescope using the following equation:


Data Sheet – Experiment 13

Part A: Refraction

Place edge of rectangular prism on line.

Data Sheet – Experiment 13 Con’t.

Part B: Lenses

1. Measured focal length.

Lens Color Code / Focal Length
f
(cm)

Red

Green

2. Calculated focal length.

Lens / Image Distance
si
(cm) / Object Distance
so
(cm) / Focal length

(cm) / % Difference of part 1 and 2 focal lengths
Red
Green

3.Magnification.

fo = cm

fe= cm

Distance between lenses:cm

M =

12-1