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?

An object is held at a distance of 60 cm from a convex mirror of focal

1.	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» Solution :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`.