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Question:

A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used. A converging lens is kept coaxially in contact with a diverging lens - both the lenses being of equal focal length. What is the focal length of the combination?

Solution:

i) Here, the distance between screen and object is D = 100 cm and the distance between two locations of the convex lens is d = 20 cm. Using the formula, the focal length f = D² - d² / 4D = 100² - 20² / 4 × 100 = 24 cm

ii) If f be the focal length of both lenses and F be the focal length of the combination, then 1/F = 1/f + 1/-f = 0
Thus, the focal length of the combination will be infinite.