JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Geometrical Optics

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is

d_{1}

from C and the distance of the image formed is

d_{2}

from C, the radius of curvature of this mirror is :

Answer: (C)

Solution

Measured from the mirror, the object lies beyond the centre of curvature at

u = - (R + d_{1})

and the real image lies between the centre and the pole at

v = - (R - d_{2})

. The mirror relation

\frac{1}{v} + \frac{1}{u} = \frac{2}{R}

gives

\frac{1}{R - d _{2}} + \frac{1}{R + d _{1}} = \frac{2}{R} .

Clearing denominators,

R (2 R + d_{1} - d_{2}) = 2 (R + d_{1}) (R - d_{2})

, which reduces to

R (d_{1} - d_{2}) = 2 d_{1} d_{2}

. Hence

R = \frac{2 d _{1} d _{2}}{d _{1} - d _{2}} .

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Single correct option