Question

The radius of curvature of the face of a plano-convex lens silvered from the plane surface is 12cm and its refractive index is 1.5. At what distance from the lens the parallel rays incident on the convex face will converge?

• A. $12cm$
• B. $15cm$
• C. $20cm$
• D. $24cm$

Answer 1

The correct option is A $12cm$

$\text{Concave Mirror}\Rightarrow \frac{1}{f}=\frac{2}{f_l}+\frac{1}{f_m}{f}_m=\infty \frac{1}{f}=\frac{2}{f_l}+\frac{1}{\infty }=\frac{2}{f_l}\frac{1}{f_l}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})\frac{1}{fl}=\left({\mu }_{ga-1}\right)\left(\frac{1}{R}\right)\frac{1}{f_l}=(\frac{3}{2}-1)\left(\frac{1}{12}\right)=\frac{1}{2}\left(\frac{1}{12}\right)=\frac{1}{24}\frac{1}{f}=\frac{2}{f_l}\frac{2}{24}=\frac{1}{12}f=12cm$
Hence the rays will coverge at a distance of 12 cm from the lens.