Download Thin Lenses

THIN LENSES
OBJECTIVE: To study and verify some of the laws of optics applicable to thin lenses by
forming images with a positive and negative lens, and by determining the focal length of the
positive lens.
THEORY: Each point of a self-luminous object (such as the Sun or the filament of a light bulb)
or reflection object (such as the Moon or you) is a source of light with a large number of rays
emanating from it in all directions. A lens will bend the direction of those rays that strike it, and
an image of the object may be formed. If a lens refracts the rays from a single point on the
object so that they converge as they leave the lens, then the rays intersect at some point in
space and a real image is formed at this same point. Real image formation is illustrated in
Figure 1. Only a positive lens can form a real image and only if the object is outside the focal
point. A virtual image is formed if the rays leaving the lens diverge. The projections of these
rays back towards the lens intersect at a single point in space. A screen placed at this point will
not reveal an image, but the image is visible to the eye at this point if observed from the proper
position. A positive lens can form a virtual image if the object is inside the focal point of the lens
as shown in Figure 2. A negative lens will always form a virtual image as shown in Figure 3.
A thin lens is one whose thickness is negligible in comparison to the image and object
distances. The object distance (p) is measured from the object to the center of the lens. The
image distance (q) is measured from the center of the lens to the image. These distances and
the focal length (f) are related by the ‘thin lens equation’:
1/p + 1/q = 1/f
(1)
Recall that the focal length is the distance from the lens to the focal point. Object distances,
image distances, and focal lengths can be positive or negative. We will see examples of both
positive and negative values in this experiment.
The ratio of the image size (h’ ) to the object size (h) can be predicted by use of the lateral
magnification (M) where
M = h' / h
(2)
If the image is inverted, then h’ is negative and the magnification is negative. Theory gives the
lateral magnification in terms of the object and image distances:
M = -q / p
(3)
p
q
h
F
O
I
h’
f
Fig. 1: Real Image (Positive Lens)
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q
q
p
p
h’
F
h
I
h
O
O
f
Fig. 2 Virtual Image (Positive Lens)
F
h’
I
f
Fig. 3 Virtual Image (Negative Lens)
Part 1: Real Image Formation With a Positive Lens
PROCEDURE:
1. Place the slide on the optical bench. By shining a light through the slide, we will use the lens
to form an image of the slide on the screen. Hence, the slide is our object in this part. The
arrows on the slide are 30 mm long, thus the object height is h = 30 mm.
2. Place the lens at some position so that it is greater than one focal length away from the
object and focus an image of the object on the screen by moving the screen. Measure object
and image distances (p& q).
3. Measure the height of the image of the arrow (h’). (If you cannot image the entire arrow
clearly, then use the large or small circle as your image and measure the diameter of this image
circle. This diameter is the value of h’. The object circles have diameters of 20 mm and 10 mm.
Use the appropriate value for h.) Notice if the image is inverted or upright compared to the
object. Notice if the image is larger or smaller than the object.
* Repeat the measurements in Steps 2-3 for at least two more object distances. You may want
to put your values in a table.
4. Place only the lens and the white screen on the optical bench and aim the lens at some
object outside the room. (If possible, perform this part of the experiment in the hallway with the
hallway lights off and with the lights in a far room on.) Move the lens or screen along the bench
until the image is focused as sharply as possible. Measure and record the image distance.
REPORT:
1. For each object distance that you used:
- calculate the focal length (f) using Eq. (1)
- calculate the magnification using Eq. (2) and then using Eq. (3)
Now answer the following questions for each object distance that you used:
Is the sign of the magnification consistent with whether the image is inverted or upright?
Is the size of the magnification consistent with whether the image is magnified or demagnified?
Do the two magnification values from Eqs. (2) & (3) agree?
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2. Are the focal lengths you calculated for the different object distances the same? Should
they be? Should focal length change with object distance? Average your focal lengths to get a
‘best’ value.
3. Does magnification depend on object distance? Does the image distance depend on the
object distance? What happens to the magnification and image distance as the object distance
decreases?
4. Does a positive lens with a large object distance act like a camera or a projector? What
about one where the object is close to the lens?
5. If the object distance is very large, then the image distance is approximately the focal length
of the lens. This is verified in the thin lens equation since as p gets big, 1/p gets small and 1/f
approaches the value of 1/q. The image distance that you measured with the ‘hall method’ in
Step 4 should therefore be close to the average focal length you calculated above. Is it?
Part 2: Virtual Image Formation With a Positive Lens
PROCEDURE:
1. Once again form a real image with the same positive lens. Now start moving the lens closer
to the object while also moving the screen to see the image. Eventually, the image will be
totally blurry once the object distance equals the focal length. In fact, a positive lens cannot
form a real or virtual image if the object is at its focal point. Now move the lens closer so that
the object is inside the focal point. Confirm that a real image cannot be formed on the screen at
any position. But if you now look through the lens at the object with your eye, you should see a
magnified, upright, virtual image. The lens is acting as a magnifying glass. The ray trace for
this situation is shown in Figure 2. Your eye is to the right of the lens and is catching the rays
that diverge from the lens. Your brain traces back the diverging rays to where they appear to
come from and ‘sees’ the image.
2. Move the lens back and forth, keeping the object inside the focal point, and observe what
happens to the size of the image as the object distance is varied.
REPORT: Record your observations as described in the Procedure.
Part 3: Virtual Image Formation With a Negative Lens
PROCEDURE:
1. Replace the positive lens with a negative lens. Confirm that a real image cannot be formed
on the screen at any position, no matter the object distance. But if you now look through the
lens at the object with your eye, you should see a smaller (demagnified), upright, virtual image.
The ray trace for this situation is shown in Figure 3. Your eye is to the right of the lens and is
catching the rays that diverge from the lens. Your brain traces back the diverging rays to where
they appear to come from and ‘sees’ the image just like with the magnifying glass.
2. Move the lens back and forth, keeping the object inside the focal point, and observe what
happens to the size of the image as the object distance is varied. Confirm that the image is
always smaller than the object.
REPORT: Record your observations as described in the Procedure.