JEE Advanced · Physics · 24. Ray Optics
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
- C \(12 \mathrm{~cm}\) to the left of the system
- D \(12 \mathrm{~cm}\) to the right of the system
Answer & Solution
Correct Answer
(C) \(12 \mathrm{~cm}\) to the left of the system
Step-by-step Solution
Detailed explanation
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
\(
\begin{aligned}
\frac{1}{v_3}-\frac{1}{60} & =\frac{1}{15} \\
v_3 & =12 \mathrm{~cm}
\end{aligned}
\)
\(
\begin{aligned}
\frac{1}{v_1}-\frac{1}{-20} & =\frac{1}{15} \\
v & =60 \mathrm{~cm}
\end{aligned}
\)
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
\(
\begin{aligned}
\frac{1}{v_3}-\frac{1}{60} & =\frac{1}{15} \\
v_3 & =12 \mathrm{~cm}
\end{aligned}
\)
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