Question

A buring candle is placed in front of a concave spherical mirror on its principal optical axis at a distance of `(4//3)F` form the pole of the mirror (here `F` is the focal length of the mirror). The candle is arranged at right angle to the axis. The image of the candle in the concave mirror impinges upon a convex mirror of focal length `2F` . The distance between the mirrors is `3F` and their axes coincide. The image of the candle in the first mirror plays the part of a virtual object with respect to the second mirror and gives a real image arranged between the two mirrors. Find the total linear magnification (magnitude only) of the system.

Answer 1

Correct Answer - 6
For reflection by concave mirror.
`(1)/(-F)=(1)/(v)+(1)/(-4F//3)`
`rArr v=-4F` Hence `m_(1)=(-v)/(u)=-3`
For reflection by concave mirror,
`u=F , f=+2F (1)/(2F)=(1)/(v)+(1)/(F) (1)/(v)=(1)/(2F)-(1)/(F)=-(1)/(2F) v=-2F`
magnification by concave mirror.
`m_(2)=-(-(2F)/(F))=2`
Net magnification `=m_(1)m_(2)=(-3)(2)=-6`