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JEE Advanced Physics Ray Optics 2022 JEE Advanced 2022 (Paper 2)

JEE Advanced Physics Question (2022) — Solution

Question

An object and a concave mirror of focal length f = 10   cm  both move along the principal axis of the mirror with constant speeds. The object moves with speed V 0 = 15   cm   s - 1  towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u . When u = 30   cm , the speed of the mirror V m  is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of V m  is _______  cm   s - 1 .

Options

  1. A. A
  2. B. B
  3. C. C
  4. D. D

Answer

A. A

Step-by-step solution

Magnification expression for concave mirror is given by, m = f f - u = - 10 - 10 - - 30 = - 1 2 For concave mirror, we can write, v i , m = - m 2 v o . m ⇒   v o - v m × m 2 + v i - v m = 0 As given in the question,  v i = 0 . Therefore,  ⇒   v o - v m × 1 4 = v m ⇒ v o = 5 v m ⇒ v m = v o 5 = 15 5 = 3   cm   s - 1

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