Physics 111: Elementary Physics
Laboratory E
Thin Lenses
1.
Introduction
A lens is a transparent object with two refracting surfaces shaped such that it can produce an
image by refracting light that comes from an object. A lens that causes parallel light rays to
converge is a converging lens; if parallel light rays are made to diverge then lens is diverging.
Converging lenses are thicker in the middle than at their ends; diverging lenses are thinner in the
middle than at their ends.
Lenses are used in many optical instruments: cameras, projectors, microscopes, telescopes,
copiers, eyeglasses etc. The theoretical study of lenses can be very complicated, however, there is
one type of lens whose properties are particularly easy to describe theoretically – thin lenses. A
thin lens is a lens with spherical surfaces in which the thickest part is thin compared to the object
and image distances and the radii of curvature of the lens. When light rays parallel to the lens axis
are incident on a converging lens they are focussed at a point known as the focal point; the
distance from the lens is known as the focal length, f.
Lensmaker’s formula:
For a thin lens, in air, the focal length f, depends on the refractive index of the lens n, and the radii
of curvature of the two surfaces of the lens R1 and R2 through the formula,
 1
1
1 

 (n  1) 
f
 R1 R2 
(1)
Lens equation:
Also, for thin lenses, the distance of the object, p, and image, q, from the lens and the focal length
f, are related by,
1 1 1
 
f
p q
(2)
Magnification:
The magnification of a lens, m, is defined by,
m
q
p
(3)
and
|m|
image height hi

object height ho
(4)
In order to use these formulas certain “sign conventions” must be followed; for example, if a lens
creates a virtual image the image distance is negative. A complete description of these
conventions may be found in your textbook and the course web pages. Conveniently, in this lab,
the situations are such that when using equations (1) – (3) the variables, f, p, q, R1, R2 are all
positive. (Notice that the magnification m, can be positive or negative. If m > 0 the image is
upright, whereas if m < 0 the image is inverted).
Image Formation:
The location and size of an image can be determined graphically, by means of the behavior of
three characteristic rays. These rays are indicated in the diagram below for a converging lens.
1
Object
Focal point
3
Axis
2
Focal point
2.
Image
Procedure
This experiment consists of two distinct parts. In the first part you will use a light source which
creates light rays to investigate the reflecting/refracting properties of a plane mirror, a spherical
mirror, a converging lens and a diverging lens. You will measure the focal length of the converging
and diverging lenses and use the lensmakers formula (1) to estimate the refractive index of the
material the lenses. The second part of the experiment uses an optical bench to measure the object
and image distances for a converging lens from which the focal length and magnification are
determined by equations (2) and (3).
Part I
1.
Plug in the light source and rotate the front of the box so that several parallel light rays leave the
source. Place the plane mirror in front of the box and sketch the behavior of the rays before and
after reflection.
2.
Sketch the behavior of the light rays before and after reflection by the spherical mirror.
3.
Sketch the behavior of the light rays before and after refraction by the converging lens.
Measure the focal length of the converging lens, f.
4.
Sketch the behavior of the light rays before and after refraction by the diverging lens. By
extrapolating the diverging rays onto the source side of the lens estimate the focal length of the
lens.
5.
Using the ruler provided, measure the thickness of the converging lens at its centre, a, and the
thickness at either of the ends, b. Measure the length of the lens, d.
b
a
d
6.
Assuming the curved surfaces of the converging lens have the same curvature, R, using simple
geometry, it is possible to obtain the following expression for R,
R
( a  b) 2  d 2
.
4 ( a  b)
(5)
Calculate the radius of curvature of the surfaces of the converging lens.
7.
Using the lensmakers formula (1), with R1 = R2 = R and your value of f for the converging
lens, evaluate the refractive index of the lens.
Part II
1.
Set up the optical bench as shown in the diagram below. The object is the arrow drawn on the
frosted glass in front of the light source.
object
Lens
image
screen
2.
Focus the image by moving the lens back and forth along the optical bench. Record the object
distance (p), object height (ho), image distance (q) and image height (hi) in the table provided.
3.
Use the lens equation (2) to determine the focal length of the lens.
4.
Use equation (3) to obtain the magnification of the lens.
5.
Use equation (4) to obtain the magnification using the heights of the image and object.
6.
Repeat steps 2-5 for two more (different) object and image distances.
7.
Obtain values of the average focal length and magnification of the lens.
8.
Write down the image properties (real, virtual, upright, inverted).
Physics 111: Elementary Physics
Pre-Lab Exercise
Thin Lenses
Name: _____________________
Section: _______
1.
Re-arrange the Lensmaker’s formula (1) to obtain the expression you will need in Part I-8 for the
refractive index, n, in terms of f and R (assume R = R1 = R2).
2.
With the values of a,b and d provided below for a converging lens (with surfaces of equal curvature)
use (5) and your expression above to fill in the blanks.
Converging lens
Centre thickness (a) = 1.35 cm
Lens length (d) = 5.5 cm
Radius of curvature (R) = ______________ cm
Focal length (f) = 12.0 cm
Refractive index of lens (n) = ____________
End thickness (b) = 0.30 cm
3.
Some typical values from a Part II experiment are given in the table below. Use the lens equation (2)
and the expressions for the magnification (3) and (4) to fill in the blanks.
Converging lens
Object (p)
cm
Image (q)
cm
32.5
Focal length
cm
ho cm
hi cm
10.4
1.1
0.34
18.4
14.1
1.1
0.86
13.0
20.7
1.1
1.73
|M| = q/p
|M| = hi/ho
Average focal length = _______________ cm
4.
What properties do you expect the image in this type of experiment to have ? Circle one of each pair
below.
REAL or VIRTUAL
5.
and
UPRIGHT or INVERTED
Sketch a ray diagram which allows you to locate the position of a real image created by a converging
lens.
Physics 111: Elementary Physics
Lab Report
Thin Lenses
Investigators:
________________________ ,
_______________________
________________________ ,
_______________________
________________________
Date: _____________
Procedure: Describe briefly (200 words or less) the procedures used in this experiment .
Data:
Part I
Plane mirror
Spherical mirror
Converging lens
Focal length (f) = ________________ cm
Diverging lens
Focal length = __________________ cm
Converging lens
Centre thickness (a) = ________________ cm
Lens length (d) = _______________ cm
Radius of curvature (R) = ______________cm
Refractive index of lens (n) = ____________
End thickness (b) = _____________ cm
Part II
Converging lens
Object (p)
cm
Image (q)
cm
Focal length
cm
ho cm
hi cm
|M| = q/p
|M| = hi/ho
Average focal length = _______________ cm
Image properties:
Discussion:
(a)
Provide an estimate of the measurement error in the focal length of the lens.
(b)
Which of the two methods of measuring the magnification is more accurate ? Explain.
(c)
With the lens fixed in position, if the object is placed a long way from the lens and gradually moved
towards the lens, describe what happens to the image.
(d)
Why is it not possible to perform Part II of this experiment to measure the focal length of a diverging
lens ?