A thin concave lens is in contact with a thin convex lens. T... | Physics | SolveeIt | Solveeit

Today, August 19

Question

A thin concave lens is in contact with a thin convex lens. The ratio of their magnitude of the focal length is 32 and the focal length of the combined lens is 30 cm. The focal lengths of the individual lenses are

A

(A) - 15 cm and + 10 cm

B

(B) - 75 cm and + 50 cm

C

(C) - 21 cm and + 14 cm

D

(D) - 30 cm and + 20 cm

Answer

(A) - 15 cm and + 10 cm

Explanation

Solution

Explanation:
Let f1 and f2 be the focal lengths of the concave lens and the convex lens, respectively.Given:|f1f2|=32|f2f1|=23⇒f2=−23f1… (i) [focal length of concave lens is-ve]When the lenses are combined, the focal length of the combination is1F=1f1+1f2[ where ,F is the focal length of the combined lens]⇒130cm=1f1−32f1⇒130cm=−12f1⇒f1=−15cmSubstituting this value of f1 in eq. (i), we getf2=−23×−15=10cmThus, f1=−15 cm and f2=10 cmHence, the correct option is (A).