A bi-convex lens of focal length 15 cm is placed in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is [2010]

Question

A bi-convex lens of focal length 15 cm is placed in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is [2010]

Smart Achievers · Accepted Answer

(2)

Focal length of the biconvex lens L is 15 cm. A small object is placed at a distance of 30 cm from the lens, i.e., at a distance of $2 f$ . Therefore, the image should form at 30 cm from the lens at $I_{1}$ .

The image $I_{1}$ acts as a virtual object for the mirror. The mirror forms an image $I_{2}$ at a distance of 20 cm in front of it.

The image $I_{2}$ acts as an object for the lens.

Here, $u = + 10 cm, f = + 15 cm$

Applying the lens formula, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\Rightarrow \frac{1}{v} - \frac{1}{10} = \frac{1}{15}$

$\Rightarrow \frac{1}{v} = \frac{1}{15} + \frac{1}{10} = \frac{25}{150}$

$∴ v = 6 cm$

Therefore, the final real image is formed at a distance of 16 cm from the plane mirror.

Solution

Q.
A bi-convex lens of focal length 15 cm is placed in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is [2010]

1 virtual and at a distance of 16 cm from the mirror

2 real and at a distance of 16 cm from the mirror

3 virtual and at a distance of 20 cm from the mirror

4 real and at a distance of 20 cm from the mirror

Want Us to Email you About Special Offers & Updates?