Download Experiment 8: Lensmaker's Equation and more Study notes Optics in PDF only on Docsity!
!
Mo del No. OS-85 15C Expe rim ent 8 : L ensm akerās Eq uation
Experiment 8: Lensmakerās Equation
Purpose
In this experiment you will determine the focal length of a concave lens in two ways:
a) by direct measurement using ray tracing and b) by measuring the radius of curva-
ture and using the lensmakerās equation.
Theory
The lensmakerās equation is used to calculate the focal length (in air or a vacuum), f ,
of a lens based on the radii of curvature of its surfaces ( R
1
and R
2
) and the index of
refraction ( n) of the lens material:
(eq. 8.1)
In this notation, R is positive for a convex surface (as viewed from outside the lens)
and R is negative for a concave surface (as in Figure 8.1).
Figure 8.
Procedure
1. Place the light source in ray-box mode on a white sheet of paper. Turn the wheel
to select three parallel rays. Shine the rays straight into the convex lens (see Fig-
ure 8.2).
Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably
without rocking.
Required Equipment from Basic Optics System
Light Source
Concave Lens from Ray Optics Kit
Other Required Equipment
Metric ruler
f
--- n ā 1
R
1
R
2
"#$%&'
(#)*+,'
-').
!
"
/)*#01)234+5.
(#)*+,'3&').
Figure 8.
!
Basic O ptics System Exp erimen t 8: Len smaker ās Eq uation
2. Trace around the surface of the lens and trace the incident and transmitted rays.
Indicate the incoming and the outgoing rays with arrows in the appropriate direc-
tions.
3. Remove the lens. To measure the focal length, use a ruler to extend the outgoing
diverging rays straight back through the lens. The focal point is where these
extended rays cross. Measure the distance from the center of the lens to the focal
point. Record the result as a negative value:
f = _______________ (measured directly)
4. To determine the radius of curvature, put the concave lens back in the path
of the rays and observe the faint reflected rays off the first surface of the
lens. The front of the lens can be treated as a concave mirror having a
radius of curvature equal to twice the focal length of the effective mirror
(see Figure 8.3).
Trace the surface of the lens and mark the point where the central ray hits
the surface. Block the central ray and mark the point where the two outer
rays cross. Measure the distance from the lens surface to the point where
the reflected rays cross. The radius of curvature is twice this distance.
Record the radius of curvature:
R = _______________
5. For this lens, it is not necessary to measure the curvature of both sides because
they are equal ( R
1
= R
2
= R ). Calculate the focal length of the lens using the lens-
makerās equation (Equation 8.1). The index of refraction is 1.5 for the acrylic
lens. Remember that a concave surface has a negative radius of curvature.
f = _______________ (calculated)
6. Calculate the percent difference between the two values of f from step 3 and
step 5:
% difference = _______________
(#)*+,'3&').
Figure 8.3: Reflected rays from
the lens surface
!
Basic O ptics System Experime nt 9 : Appa rent Depth
Figure 9.
2. With both eyes, look down through the top of the trapezoid. Does the line viewed
through the trapezoid appear to be closer? Close or cover one eye, and move your
head side to side. Do you see parallax between the line viewed through the trape-
zoid and the line viewed directly?
3. In this step, you will hold a pencil near the trapezoid to determine the position of
the apparent line. When the pencil and the apparent line are at the same distance
from your eye, there will be no parallax between them.
While looking down through the trapezoid (with one eye), hold a very sharp
pencil as shown in Figure 9.3 so it appears to be lined up with the line inside the
trapezoid. Move your head left and right to check for parallax. Move the pencil
up or down and check again. When there is no parallax, mark that point. (Hold
the trapezoid with your free hand, press the pencil tip gently against the side of
the trapezoid and twist the pencil to make a light mark. Erase the mark after you
have finished this experiment.)
Analysis
1. Measure the distance from the top of the trapezoid to your pencil mark. Record
this apparent depth, d , in the first row of Table 9.1.
2. Measure the thickness, t , of the trapezoid and record it in Table 9.1. 3. Use Equation 9.1 to calculate the index of refraction and record your result in
Table 9.1.
Part 2: Ray-tracing Method
Procedure
1. Place the light source in ray-box mode on a white sheet of paper. Turn the wheel
to select five parallel rays. Shine the rays straight into the convex lens. Place the
mirror on its edge between the ray box and the lens so that it blocks the middle
three rays, leaving only the outside two rays (as in Figure 9.4, but do not put the
trapezoid there yet).
Note: The lens has one flat edge. Place the flat edge on the paper so the lens stands stably
without rocking.
Table 9.1: Results
d t n
Part 1: Parallax method
Part 2: Ray-tracing method
Trapezoid
-##
9#:)
;#&937')*1&
.61&&
<#,'3'5'
.19'36#3.19'
Figure 9.
!
Mo del No. OS-85 15C Exp erimen t 9 : Ap pare nt Depth
2. Mark the place on the paper where the two rays cross each other. 3. Position the trapezoid as shown in Figure 9.4. The ābottomā surface of the
trapezoid must be exactly at the point where the two rays cross. The crossed
rays simulate rays that originate at an object on the ābottomā of the block.
4. Trace the trapezoid and trace the rays diverging from the ātopā surface. 5. Remove the trapezoid and light source. Trace the diverging rays back into
the trapezoid. The point where these rays cross (inside the trapezoid) is the
apparent position of the ābottomā of the trapezoid when viewed through the
ātopā.
Analysis
1. Measure the apparent depth, d , and record it in Table 9.1. 2. Use Equation 9.1 to calculate the index of refraction and record your result
in Table 9.1.
Questions
1. Of the two methods that you used to determine d , which one is more precise?
Explain.
2. The accepted value of the index of refraction of acrylic is n = 1.49. What was the
percent difference between the accepted value and each of your two results?
(#),'=
&').
<144#
#)3'92'
%#66#0?
3.$4@+*'
6#7?
3.$4@+*'
Figure 9.
!
Basic O ptics System Exp erimen t 14 : Vir tual Im ages
4. Look through the lens toward the light source (see Figure 14.1). Describe the
image. Is it upright or inverted? Does it appear to be larger or smaller than the
object?
________________________________________________________________
________________________________________________________________
________________________________________________________________
5. Which do you think is closer to the lens: the image or the object? Why do you
think so?
________________________________________________________________
________________________________________________________________
________________________________________________________________
6. Place the +200 mm lens on the bench anywhere between the 50 cm and 80 cm
marks. Record the position here. _____________
7. Place the viewing screen behind the positive lens (see Figure 14.2). Slide the
screen to a position where a clear image is formed on it. Record the position
here. _____________
Figure 14.
The real image that you see on the screen is formed by the positive lens with the vir-
tual image (formed by the negative lens) acting as the object. In the following steps,
you will discover the location of the virtual image by replacing it with the light
source.
8. Remove the negative lens from the bench. What happens to the image on the
screen?__________________________________________________________
9. Slide the light source to a new position so that a clear image is formed on the
screen. (Do not move the positive lens or the screen.) Write the bench position of
the light source here. _____________
Figure 14.
-12A
.#$4*'
HIEE300 G*4'')
-').
J9K$.636#
@#*$.310+2'
BCDE
-').
CE30 FE30 DE3036#3LE3
-12A
.#$4*'
HIEE300 G*4'')
-').
J9K$.636#
@#*$.310+2'
!
Mo del No. OS-85 15C Expe rimen t 1 4: Virtua l Im ages
Analysis
The current position of the light source is identical to the previous position of the vir-
tual image.
1. Calculate the virtual image distance d
i
(the distance between the negative lens
and the virtual image). Remember that it is a negative. Record it in Table 14.1.
2. Calculate the magnification and record it in Table 14.1.
(eq. 14.1)
Questions
1. How do you know that the current position of the light source is identical to the
position of the virtual image when the negative lens was on the bench?
2. In step 5 of the procedure, you predicted the position of the virtual image relative
to the light source. Was your prediction correct?
3. Is M
1
positive or negative? How does this relate to the appearance of the image?
4. Draw a scale diagram showing the light source in its original position, both
lenses, the screen, and both images. Label every part.
5. Draw another diagram at the same scale showing the light source in its final posi-
tion, the positive lens, the screen, and the image.
Part II: Virtual Image Formed by a Convex Mirror
In this part, you will find the location of a virtual image formed by convex mirror.
Procedure
1. Stick a piece of tape to the viewing screen and draw a vertical line on it as shown
in Figure 14.4.
2. Place the half-screen on the bench near one end. Turn the screen so its edge is
vertical (see Figure 14.5).
3. Place the concave/convex mirror on the bench, about 20 cm from the half-screen,
with the convex side facing the half-screen.
Table 14.1: Negative Lens
d
o
d
i
M
1
M
1
d
i
d
o
Figure 14.
Figure 14.
!
Mo del No. OS-85 15C Expe rimen t 1 4: Virtua l Im ages
3. Use d
o
and d
i
to calculate the magnification and record it in Table 14.1.
Questions
1. Is the magnitude of d
i
less than or greater than d
o
? If you replace the convex mir-
ror with a plane mirror, what would be the relationship between d
i
and d
o
2. Is M positive or negative? How does this relate to the appearance of the image? 3. Draw a scale diagram showing the half-screen, mirror, viewing screen, and vir-
tual image. Label every part.
Table 14.2: Convex Mirror
d
o
d
i
M
