Optics Problems - Numerical 08

08.

(a) A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.

(b) Suppose the object in (a) above is an illuminated slit in a collimator tube so that it is hard to measure slit size and its distance from the screen. Using a convex lens, one obtains a sharp image of the slit on a screen. The image size is measured to be 4.6 cm. The lens is displaced away from the slit and at a certain location, another sharp image of size 1.7 cm is obtained. Determine the size of the slit.

Suggested solution:

(a) Distance between object and image, D = 90 cm

Distance through which lens is displaced, d = 20 cm

Now, D = u + v = 90 cm; d = u v = 20 cm

\ u = 55 cm or 35 cm and v = 35 cm or 55 cm

(b) For first location of lens, u₁ = x and v₁ = y

For second location of lens, u₂ = y and v₂ = x

or