Answer to Question #147316 in Optics for sam

Question

.A small convex mirror is placed 60 cm from the pole and on the axis of a large concave mirror of radius of curvature 200 cm.The position of the convex mirror is such that a real image of distant object is formed on the plane of a hole drilled through the concave mirror at its pole. Calculate ‘R’ of convex mirror and height of the real image if distant object forms 0.5 degree angle at the pole of the concave mirror.

Answer 1

As per the question,

Distance between convex and concave mirror is =60cm

Radius of the concave mirror (R) = 200cm

For the concave mirror, $u=\infty$

So, $V = \frac{R}{2}=100cm$

which will act as the object for the convex mirror and the final image is on the pole of the concave mirror, and distance between convex and concave mirror is 60cm

hence,

u_1=60-100 =-40cm

Hence, object will be behind the convex mirror

$\frac{1}{f}=\frac{1}{40}+\frac{1}{60}$

$\Rightarrow \frac{1}{f}=\frac{3+2}{120}$

$\Rightarrow f=\frac{120}{5}cm$

$\Rightarrow f = 24cm$

Hence, the radius of the convex mirror is 48cm