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A screen is placed D cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by d cm. Derive the formula for the focal length of the lens.


A screen is placed D cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by d cm. Derive the formula for the focal length of the lens.


Grade:

1 Answers

Ramesh V
70 Points
11 years ago

Distance between object and image, = D cm

Distance through which lens is displaced, = d cm

Now, D = u + v ; d = u - v

or    D = u + v ; d = v - u

where u = object distance and v= image distance

1/f = 1/u + 1/v

as (v+u)2 = (v-u)2 +4vu i.e., D2 -d2 = 4vu

f = vu/(v + u)

 focla length  =(D2 - d2)/4D

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regards

Ramesh

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