Question

When the plane surface of a planoconvex lens of refractive index $1.5$ is silvered, it behaves like a concave mirror of focal length $30cm$. When its convex surface is silvered, it will behave like a concave mirror of focal length

• A. $10cm$
• B. $20cm$
• C. $30cm$
• D. $45cm$

Answer 1

The correct option is A $10cm$

When plane surface is silvered the focal length $f_1$ is given by
$\frac{1}{f_1}=\frac{2(\mu -1)}{R}$
Symbols having usual meanings.
But when the convex surface is silvered focal length $f_2$ becomes
$f_2=\frac{2\mu }{R}$
Dividing the last two equations we have
$\frac{f_2}{f_1}=\frac{(\mu -1)}{\mu }=\frac{1.5-1}{1.5}=\frac{1}{3}$
$f_2=\frac{f_1}{3}=\frac{30}{3}=10cm$