Download Lenses - WFU Physics

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 raytracing; 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)

1
2
k
1
2
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
n1 sin1  n2 sin 2
(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
P1 and P2. The observer views these
pins through the glass, and then places
a third pin at P3 so that, when seen
through the glass, the 3 pins are
aligned. Actually the line of light
12-1
connecting P1, P2 and P3 is bent at the first and second surfaces of the glass. These
positions P1, P2 and P3, along with the normal to the first surface, enable one to measure
the angles θ1 and θ2.
If n2 > n1, the beam of light is bent toward the normal at the first surface in Figure
2. However if n2 < n1, 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.
Air
Air
P3
P2
P2
P3
P1
Glass
P1
Glass
Figure 3: Refraction through a prism.
Figure 4: Total internal reflection.
Note: The index of refraction of a medium with respect to air is commonly called n. Since nair is 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
12-2
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.
Diverging Lens
Converging Lens
Parallel Ray
Object
Ce
n tr
Parallel Ray
al R
Focal Point
ay
Optical Axis
Object
Optical Axes
Real Image
Ce
n tra
Focal Point
Virtual Image
Figure 5: Ray diagram of a converging lens.
lR
ay
Figure 6: Ray diagram of a diverging 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:
a. passes through the focal point, if the lens is converging
b. seems to originate from the focal point, if the lens is diverging.
2. 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.
3. 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
1
f

1
so

1
(3)
si
12-3
where so is the 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;
1
1
1


(4)
f
f
f
1
2
where f1 and f2 are 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.
2. 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?
3. 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.
a. Place screen on end of optical bench opposite the window.
b. Place one lens holder on optical bench and insert lens.
c. Move lens back and forth on optical bench until you have the best image of a
distant object.
12-4
d. 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.
e. Repeat for remaining lens.
2. Confirm Equation (3) for both lenses.
a. Add the light source to the optical bench on the opposite end from the screen.
b. Measure and record the image distance, si.
c. Measure and record the object distance, so.
d. Calculate f and compare to the f measured previously.
e. Repeat for remaining lens.
3. Using so and si found above and the calculated f, draw a to-scale ray diagram for each
lens (in cm!).
4. Build a simple telescope.
a. Remove the screen and light source from the optical bench.
b. Add a second lens holder.
c. Put the longer focal length lens in the lens holder closer to the window. This is
the objective of the telescope.
d. Put the shorter focal length lens in the other holder. This lens is the eyepiece.
e. 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.)
f. Measure and record the distance between the two lenses.
g. Calculate the magnification of your telescope using the following equation:
M 
fo
fe
12-5
Data Sheet – Experiment 13
Part A: Refraction
Place edge of rectangular prism on line.
12-6
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
1 1 1
 
f
si so
(cm)
% Difference
of part 1 and 2
focal lengths
Red
Green
3.Magnification.
fo =
cm
fe =
cm
Distance between lenses:
cm
M=
12-7
12-8