Question

A converging beam of the light forms a sharp image on a screen. A lens is placed in the path of the beam, the lens being $10cm$ from the screen. It is found that the screen has to be moved $8cm$ further away from the lens to obtain a sharp image. Find the focal length and nature of lens.

• A. $12.5cm$
• B. $20cm$
• C. $13cm$
• D. $22.5cm$

Answer 1

The correct option is D $22.5cm$

Given: A converging beam of the light forms a sharp image on a screen. A lens is placed in the path of the beam, the lens being 10cm from the screen. It is found that the screen has to be moved 8cm further away from the lens to obtain a sharp image.

To find the focal length and nature of lens

Solution:

As the lens is moved away to obtain a sharp image, it means the lens is a diverging lens.

The point object acts as a virtual object and the lens forms a real image at I

$\therefore ,u=-10cm$

and $v=+18cm$

Now, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{f}=\frac{1}{18}+\frac{1}{(-10)}⟹\frac{1}{f}=\frac{10-18}{180}=\frac{-8}{180}⟹f=-22.5cm$

and it is a concave lens.