Question

An equiconvex lens of focal length 20 cm is silvered at one surface will behave as a mirror .The magnitude of focal length of that mirror is

Answer 1

An equiconvex lens of focal length 20 cm is silvered at one surface will behave as a mirror.

so, $P=2P_L+P_M$

power of lens, $P_L=\frac{1}{f_L(\textbf(in m)}}$

given, Focal length of convex lens , $f_L$ = 20cm or, 0.2m

so, power of lens, $P_L=\frac{1}{0.2}=5D$

again,

power of mirror, $P_M=-\frac{1}{f_M}$

focal length of mirror, $f_M$ = -20cm or -0.2m

so, power of mirror, $P_M$ = +5D

now, P =2 × 5D + 5D = +15D

or, -1/F = 15

or, F = -1/15 = -100/15 = -20/3 = -6.67 cm

hence, focal length of that mirror is -6.67cm