Question

An object 1cm tall is placed 4cm infront of a mirror. In order to produce an upright image of 3cm height one needs a(a) Convex mirror of radius of curvature 12cm(b) Concave mirror of radius of curvature 12cm(c) Concave mirror of radius of curvature 4cm(d) Plane mirror of height 12cm

Answer 1

answer : option (b) b Concave mirror of radius of curvature 12cm.

explanation : height of object , h = 1cm

object distance, u = -4 cm

An upright image of height 3cm is formed

so, height of image , h' = 3cm

use formula , magnification , m = -v/u = h'/h

or, -v/(-4 cm) = 3cm/1cm

or, v/4cm = 3

hence, v = 12cm

now, 1/v + 1/u = 1/f

or, 1/12 + 1/-4 = 1/f

or, 1/12 - 3/12 = 1/f => f = -6cm

hence focal length , f = -6cm

here negative sign indicates that mirror is not other than concave mirror.

so, radius of curvature of concave mirror , R = 2f = 12cm

Answer 2

Answer:

Given,

Given,h0=1cm;hi=3cm

Given,

h0=1cm;

hi=3cm

u=−4cm

m=h0/h1=13=3

m=v/v=3⇒v=3u

1/f = 1/v + 1/ u

f=−6cm

The mirror must be concave mirror of focal length 6 cm i.e.,

R=2f=12cm