Lenses

These are two types:
(i) Convex/converging lenses
(ii) Concave/diverging lenses
Convex lens

Concave lens

Terms used:

1. Principal axis: is a line joining the principal focus and the optical Centre
2. Principal focus of a convex lens: is a point on the principal axis to which all rays originally parallel and close to the principal axis converge after refraction by the lens
3. Principal focus of a concave lens: this is a point on the principal axis to which all rays originally parallel and close to the principal axis appear to diverge after refraction by the lens

4. Focal length: this is the distance between the principal focus and the optical centre
5. Optical centre: this is the centre of the lens at which rays pass undeviated.

Construction of ray diagram

In constructing ray diagrams, 2 of the 3 principal rules are used.
1. A ray parallel to the principal axis is refracted through the focal point

2. A ray through the optical centre passes through undeviated i.e. is not refracted

3. A ray through the principal focus emerge parallel to the principal axis after refraction

Images formed by convex lenses
The nature of the image formed in a convex lens depends on the position of the object from the lens
a. Object beyond 2f

b. Object at 2f

c. Object between f and 2f

d. Object at f

e. Object between F and C

When the object is placed between f and c, the image is magnified and this is why the convex lens is known as a magnifying glass
Image Formation in a Concave Lens

Power of a lens
It is defined as the reciprocal of focal length in metres
Power of lens = where f is focal length of the lens in metres
S.I units of power of the lens is dioptres (D)
Example
1. Calculate the power of the focal length 10cm.
P = =
= 10D
2. Find the power of the lens whose focal length is 20cm
P = =
= 50D

Magnification of the lens
It is defined as the ratio of the image height to object height
M =
OR
It is the ratio of image distance to object distance from the lens
M = where v – image distance
U – Object distance

Determination of image position by graphical method
Same rules are used
A lens is represented by a line on a graph paper. Scale must be used.
Example
Object 5cm tall is placed 15cm away from a lens of focal length 10cm. By construction;

Determine the position, size and nature of the final image (use a scale 1cm: 5cm)
Question

1. A simple magnifying glass of focal length 5cm forms an erect image of the object 25cm from the
lens. By graphical method
a. Find the distance between the object and image
b. Calculate the magnification
2. An erect object 5cm high is placed at a point 25cm from a convex lens. A real image of the object is formed 25 cm high. Construct a ray diagram and use it to find the focal length of the lens
3. An object is placed at right angle to the principal axis of a thin covering lens of focal length 10cm.
A real image of height 5cm is formed at 30cm from the lens. By construction, find the position and height of the object (use 1cm: 5cm)

Determination of focal lens of a convex lens
a) Method 1: Rough method
Procedure
A converging lens with a screen on one side is placed some distance from the distant object e.g. a window as shown.

The screen is moved away or towards the lens until a clear image of the window is formed on the screen
The distance between the lens and the screen is measured and this is its focal length f
N.B – the value of f obtained by the above method is not very accurate because rays of light from the window are assumed to be parallel but may not be perfectly parallel.

b) Determination of focal length using on illuminated object

Procedure
– A lens is set up in a suitable holder with a plane mirror behind it so that light passing through the lens is reflected back as shown above
– Across wire is used as the object in a hole of a white screen. It is illuminated by the bulb
– The position of the lens is adjusted until a sharp image of the object is formed on the screen
alongside the object
– The distance between the lens and the screen is measured, this gives the focal length of the lens
c) Using lens formula method
– The lens is set up in front of an illuminated object so that a real image is formed on a white screen placed on the opposite side.
– The lens is then adjusted so that the image is sharply in focus.
– The object distance u and image distance v from the lens is measured

– Several pairs of values of u and v are found and the results entered in a suitable table, including
values of and the mean value of = + determined.
– Focal length is calculated from: f =

Application of lenses
Lenses are used in
 Lens camera
 Slide projectors
 Spectacles (used by people with eye defects)
 Microscopes and telescopes.