Question

An object is held at a distance of 60 cm from a convex mirror of focal length 20 cm. At what distance from the convex mirror, should a plane mirror be held so that images in the two mirrors coincide?

Answer 1

For convex mirror, `u = -60 cm, f = +20 cm`.

From mirror formula, `(1)/(v) =(1)/(f) - (1)/(u) = (1)/(20) + (1)/(60) = (3+1)/(60) = (1)/(15)`
`v = 15 cm`. `:. PI =15 cm`.
Let the plane mirror be held at `M` so that images in the two mirrors coincide.
As `OM = MI = MP +PI = x+15`
and `OM = (1)/(2)OI = (1)/(2)(60+15) = 37.5 cm`.
`:. x + 15 = 37.5, x = 37.5 -15 = 22.5 cm`.