An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

Question

An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror? (A) 25 cm (B) 7 cm (C) 18 cm (D) 27 cm

Tardigrade Admin · Accepted Answer

As shown in figure, the plane mirror will form erect and virtual image of same size at a distance of

30 c m

behind it. So the distance of image formed by plane mirror from convex mirror will be

P I = M I - MP

But as,

M I = MO

P I = MO - MP = 30 - 20 = 10 c m

Now as this image coincides with the image formed by convex mirror, therefore for convex mirror,

u = - 50 c m; v = + 10 c m

So,

\frac{1}{+ 10} + \frac{1}{- 50} = \frac{1}{f}

i.e.,

f = \frac{50}{4} = 12.5 c m

So,

R = 2 f = 2 \times 12.5 = 2 c m