# Diverging Lens

A diverging lens with focal length of 25 cm is used to view a postage stamp 50 cm from the lens. (a) How far from the lens does the stamp appear? (b) What is the magnification of the image? Work this problem by ray tracing?

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Please see the attached file.

SOLUTION

C

A B

O Principle Axis

F

v D

f

u

Fig. shows a diverging lens (concave lens). F is its focal point and O the optical centre. An object (stamp in the present problem) is placed on the principle axis at a distance u from O. Let us consider a ray starting from the upper most point of the object and going parallel to the principle axis. Any ray incident on the diverging lens parallel to the principle axis emerges such that it appears to be coming from the focal point F (ray ABC). Another ray starting from the same point passes through the optical centre O and follows a straight path (AOD). A virtual, erect image is formed at the point of intersection of the two rays. This image is formed at a distance v on the same side of the lens as the object.

u,v and f are related to each other by the equation : 1/u - 1/v = 1/f ........(1)

In applying (1) following sign convention is to be follows :

1. All distances are to be measured from the optical centre O.

2. A distance measured in the direction of the incident ray is +ve and that measured in opposite direction is -ve.

Based on the above sign convention we have the following distances for the present problem :

u = -50 cm

f = -25 cm

Applying (1) we get : 1/v - (-1/50) = - 1/25

Or 1/v + 1/50 = - 1/25

Or 1/v = - 3/50

Or v = - 50/3 = - 16.67 cm

Magnification m = v/u = 16.67/50 = 0.33

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