A thin cylindrical rod of length 10 cm is placed horizontally on the principal axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid-point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be 3 x cm. The value of x i $s__________.$
Options

Question

A thin cylindrical rod of length 10 cm is placed horizontally on the principal axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid-point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be 3 x cm. The value of x i $s__________.$

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: Use the spherical-mirror relation 1/f = 1/v + 1/u with m = - v/u and R = 2f, following the Cartesian sign convention. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is 32. Therefore the correct option is A.