Question

A biconvex lens of focal length $15cm$ is in front of a plane mirror. The distance between the lens and the mirror is $10cm$ . A small object is kept at a distance of $30cm$ from the lens. The final image is

• A. Virtual and at a distance of $16cm$ from the mirror
• B. Real and at a distance of $16cm$ from the mirror
• C. Virtual and at a distance of $20cm$ from the mirror
• D. None of the above

Answer 1

Answer: (B)

Object is placed at distance $2f$ from the lens. So first image $I$ will be formed at distance $2f$ on other side. This image $I_1$ will behave like a virtual object for mirror. The second image $I_2$ will be formed at distance $20cm$ in front of the mirror, or at distance $10cm$ to the left hand side of the lens.
Now applying lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$


$\therefore \frac{1}{v}-\frac{1}{+10}=\frac{1}{+15}$
$orv=16cm$
Therefore, the final image is at distance $16cm$ from the mirror. But, this image will be real.
This is because ray of light is travelling from right to left.