A point object is placed at distance of $20 \mathrm{~cm}$ from a thin planoconvex lens of focal length $15 \mathrm{~cm}$. The plane surface of the lens is now silvered. The image created by the system is at

• A

  $60 \mathrm{~cm}$ to the left of the system
• B

  $60 \mathrm{~cm}$ to the right of the system
• Correct answer
  C

  $12 \mathrm{~cm}$ to the left of the system
• D

  $12 \mathrm{~cm}$ to the right of the system

Solution

Refraction from lens $$ \begin{aligned} \frac{1}{v_1}-\frac{1}{-20} & =\frac{1}{15} \\ v & =60 \mathrm{~cm} \end{aligned} $$
i.e., first image is formed at $60 \mathrm{~cm}$ to the right of lens system. Reflection from mirror After reflection from the mirror, the second image will be formed at a distance of $60 \mathrm{~cm}$ to the left of lens system. Refraction from lens $$ \begin{aligned} \frac{1}{v_3}-\frac{1}{60} & =\frac{1}{15} \\ v_3 & =12 \mathrm{~cm} \end{aligned} $$

Hence, the correct answer is option: 'C'.