Question

The rear face of an equiconvex lens of focal length 30 cm is silvered so that if behave like a concave mirror.The focal length of mirror is $({\mu }_{lens}=\frac{3}{2})$

• A. 7.5 cm
• B. 15 cm
• C. 30 cm
• D. 20 cm

Answer 1

The correct option is B 15 cm

Given, $f=30cm$

$\mu =\frac{3}{2}$

Since it is an equiconvex lens $R_1=R_2=R$

Also $R_2$ will negative if we follow the sign convention of light rays travelling through a lens or mirror.

Applying the lens makers formula we get

$\frac{1}{f}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$\Rightarrow \frac{1}{30}=\left(\frac{3}{2}-1\right)\left(\frac{1}{R}+\frac{1}{R}\right)$

$\Rightarrow \frac{1}{30}=\frac{1}{2}\times \frac{2}{R}=\frac{1}{R}$

$\therefore R=30cm$

For a concave mirror we know that

$f=\frac{R}{2}=\frac{30}{2}=15cm$

Hence the correct answer is option (B).