Question

A point object is placed at a distance of $20cm$ from a thin planoconvex lens of focal length $15cm$, if the plne surface is silvered. The image will form at

• A. $60cm$ left of $AB$
• B. $30cm$ left of $AB$
• C. $12cm$ left of $AB$
• D. $60cm$ right of $AB$

Answer 1

The correct option is C $12cm$ left of $AB$

Refraction from lens : $\frac{1}{v_1}-\frac{1}{-20}=\frac{1}{15}$

$\Rightarrow \frac{1}{v_1}=\frac{1}{60}$

$\Rightarrow v_1=60$

i.e, first image is formed at $60cm$ to the right of lens system.

Now, reflection from plane mirror - the second image will be formed at a distance $60cm$ to the left of the lens system.

Again reflection from lens :-

$\Rightarrow \frac{1}{v_3}=\frac{1}{60}-\frac{1}{15}$

$\Rightarrow \frac{1}{v_3}=\frac{1}{12}$

$\Rightarrow v_3=12$

Therefore, the final image is formed at $12cm$ to the left of the lens system. Hence, the answer is $12cm$ left of AB.