The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is 40 cm . The area of the image is 9 times that of the square.

Question

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is 40 cm . The area of the image is 9 times that of the square. The focal length of the lens is :

TestHub · Accepted Answer

If side of object square = ℓ and side of image square = ℓ ′ From question, ℓ ℓ ′2 ​ = 9 or ℓ ℓ ′ ​ = 3 i.e., magnification m = 3 u = − 40 cm v = 3 × 40 = 120 cm f = ? From formula, v 1 ​ − u 1 ​ = f 1 ​ ​ 120 1 ​ − − 40 1 ​ = f 1 ​ or, f 1 ​ = 120 1 ​ + 40 1 ​ = 120 1 + 3 ​ ∴ f = 30 cm ​

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