Experiment 18U: Thin Lens Equation
Purpose
(1) To observe images formed by lenses; to practice focusing.
(2) To measure the focal lengths of lenses, using the Thin Lens Equation.
Apparatus
(a) Optical bench, with mounted lamp and screen.
(b) A set of 3 lenses, color-tagged RED, YELLOW, and BLUE; two lens mounts.
(c) A desk lamp.
Theory
A thin lens is characterized by its focal length f. The
BASIC EQUATION
object distance S, the image distance S´, and the focal
1
1
1
(1)
length are related by (1), the Thin Lens Equation.
+ =
Equation (1) can be used for all kinds of thin lenses,
S' f
S
provided the following sign-conventions are observed.
(i) f is positive for converging lenses, negative for diverging lenses.
(ii) S is positive if the object is in front of the lens, according to the direction of
light rays. But if the object is behind the lens ( = virtual object) then S is
negative.
(iii) S´ is positive if the image is behind the lens, and negative if it is in front of the
lens ( = virtual image).
Formula (1) and the sign conventions can be used for a succession of lenses, with the
principle: the image formed by a preceding lens (according to the direction of light rays!)
serves as an object for the following lens.
Preliminary Procedure
Familiarize yourself with the Optical Bench. Your instructor should explain the
details to you.
At all times during the experiment, make sure that:
(i) The centers of all lenses and the center of the lamp are aligned along a (horizontal)
optical axis.
(ii) The planes of all lenses are perpendicular to the optical axis; the same applies to
the screen and the lamp.
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Experiment 18U
Procedure Part I: Measuring f of a Converging Lens
(a) Place the lamp (the primary object) at the position xo = 0.0 c,; it should remain
there through all parts of the experiment.
Record your sample-number on your data-sheet. Use only the lenses belonging
to your sample
.
(b) Prepare a table on your data-sheet as shown in Fig.1.
RED LENS DATA
RUN
#
RED LENS
POSITION
XR (cm)
SCREEN
POSITION
XSCR (cm)
FOCAL
LENGTH
fR ( cm)
1
2
3
4
5
6
7
8
AVERAGE < fR >
(c) Place the RED lens about 12 to 13cm from the lamp and record its position, within
1 millimeter accuracy, as xR, under Run #1. Then place the screen behind the lens
and move it back-and-forth until you observe the image to be sharp and
undistorted; this process is known as focusing.
(CALL YOUR INSTRUCTOR IF IN DOUBT)
(d) Repeat (c) for additional seven runs (for a total of 8 runs) with xR ranging from 11 to
25 cm, evenly spaced. Record xR and xSCR in the table.
(e) From the Basic Equation (1) and the particular
situation in Fig. 1, one can derive a “Handy
Formula” (2). Use it to complete, on your
data-sheet, the Red Lens Table; calculate
the average value < fR >.
(2)
HANDY FORMULA
(Valid Only for Fig.1)
fR = ( xSCR – xR ) xR
xSCR
(f) Optional (consult your Instructor): Make a direct measurement of fR by focusing a
far-away object onto the screen.
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Experiment 18U
DO NOT PROCEED FURTHER UNTIL YOUR INSTRUCTOR CHECKS AND
APPROVES YOUR RESULTS.
Procedure Part II: Image Formed by Two Converging Lenses
(g) Place the RED lens at twice its focal length from the lamp; clamp it securely and
record its position as xR. Locate the image (using the screen) and record its position
as xKEY.
During the remainder of the experiment the position of this image (xKEY) shall not
be changed.
(h) Remove the screen. Keep in mind that the image is still there, at xKEY. Place the
YELLOW lens about 10 to 12cm beyond xKEY.
The image at xKEY now serves as the object for the YELLOW lens.
Place the screen beyond the YELLOW lens and locate the new image, as sharp
and undistorted as possible. On your data-sheet, prepare a table:
Original
YELLOW
LENS
Position
Run #
1
2
3
YELLOW LENS DATA:
xSCR
REVERSED
xY (cm)
(cm)
YELLOW
LENS
Position
Run #
xY (cm)
xSCR
(cm)
4
5
6
Record the position xY of the YELLOW lens and of the image xSCR under
Run #1. Repeat, by moving the YELLOW lens back-and-forth, and re-focusing the
image, for a total of 3 runs.
(i) Reverse the yellow lens in its holder, make additional three runs and record all
data. (The reason for reversing is that the center of the YELLOW lens does not
exactly correspond to the plane of the lens-holder).
(j) Optional (Consult your Instructor): Make a direct measurement of fY by focusing a
far-away object onto the screen. Make sure you make two such measurements, one of
them in reversed position. Calculate the average value.
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Experiment 18U
Procedure Part III: The Diverging Lens
(k) Make sure that your RED lens is still in the same position as in Part II, so that there
is still an image at xKEY, which will again serve as your object. Mount the Blue
lens and make sure it is properly aligned. Place the BLUE lens about 6 or 7cm in
front of xKEY position. Next, move the screen and locate the image as sharp and
undistorted as possible (usually, this will be possible only for the central portion of
the image). On your data-sheet, prepare a table similar to that for the yellow lens.
Part II (h). Make and record three runs in original and three more in reversed
mounting.
Lab Report
Part I
1) Calculate fR.
2) Show, by algebra, why the formula (2) follows from the equation (1), for the situation
in Fig. 1.
3) If you have done the focusing of a far-away object onto the screen, display the
%-discrepancy between <fR> from (e) from (f).
Part II
4) Draw a diagram of your experimental set-up, similar to Fig. 1, showing clearly all five
positions:
xo , xR , xKEY , xY, xSCR
Display the formulae from which you will calculate S and S΄ for the YELLOW lens in
terms of xY , xKEY, and xSCR.
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Experiment 18U
5) Copy and complete the table below:
CALCULATION of fY (FOCAL LENGTH OF YELLOW LENS)
Original
YELLOW
LENS
Position
Run
#
S
S΄
1
2
3
AVE:
6)
fY
REVERSED
YELLOW
LENS
Position
Run
#
S
S΄
fY
4
5
6
AVE:
OVERALL AVERAGE < f Y > =
(i) Comment on the discrepancies between the values of fY in individual runs. If
they are large, figure out the reason.
(ii) Comment on the difference between the averages for the original and the
reversed mountings of the lens.
Part III
7) Draw a diagram of your experimental set-up, similar to Fig. 1, showing clearly all five
positions:
xo , xR , xKEY , xB, xSCR
Display the formulae from which you will calculate S and S´ for the BLUE lens, in
terms of xB, xKEY, and xSCR.
8) Set up and complete a table, using the +/- sign convention, similar to that for the
yellow lens (in Part II above).
9) Comment on all discrepancies and figure out the reasons for them.
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