A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by the successive reflections, first at concave mirror and then at convex mirror.

Question

A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by the successive reflections, first at concave mirror and then at convex mirror. (A) 12 cm behind convex mirror, real (B) 9 cm behind convex mirror, real (C) 6 cm behind convex mirror, virtual (D) 3 cm behind convex mirror, virtual

Tardigrade Admin · Accepted Answer

According to given problem, for concave mirror,

u = - 15 c m

and

f = - 10 c m

\frac{1}{v} + \frac{1}{- 15} = \frac{1}{- 10}

i.e.,

v = - 30 c m

i.e., concave mirror will form real, inverted and enlarged image

I_{1}

of object

O

at a distance

30 c m

from it, i.e., at a distance

40 - 30 = 10 c m

from convex mirror.
For convex mirror the image

I_{1}

will act as an object and so for it

u = - 10 c m

and

f = + 15 c m

.

\frac{1}{v} + \frac{1}{- 10} = \frac{1}{15}

i.e.,

v = + 6 c m

So final image

I_{2}

is formed at a distance

6 c m

behind the convex mirror and is virtual as shown in figure.