Question

A convex lens with a focal length of 12 cm has an object at a distance of 20 cm in front of the lens. A blurred image is obtained on the screen placed at a distance of 23 cm in front of the lens. In order to obtain a clear image, the screen has to be moved ______.

विकल्प

• towards the lens.

• away from the lens.

• to a position very far from the lens.

• either towards or away from the lens.

Answer 1

A convex lens with a focal length of 12 cm has an object at a distance of 20 cm in front of the lens. A blurred image is obtained on the screen placed at a distance of 23 cm in front of the lens. In order to obtain a clear image, the screen has to be moved away from the lens.

Explanation:

Given: Focal length (f) = 12 cm (Positive for a convex lens.)

Object distance (u) = −20 cm (Negative because the object is in front of the lens.)

The lens formula for a convex lens is given by:

`1/f = 1/v - 1/u`

⇒ `1/v = 1/12 + 1/-20`

⇒ `1/v = 1/12 - 1/20`

⇒ `1/v = (1 xx 5)/(12 xx 5) - (1 xx 3)/(20 xx 3)`

⇒ `1/v = 5/60 - 3/60`

⇒ `1/v = (5 - 3)/60`

⇒ `1/v = 2/60`

⇒ `1/v = 1/30`

v = 30 cm 

∴ The actual image distance (v) is 30 cm.

Since the required image distance (30 cm) is greater than the current screen position (23 cm), the screen must be moved to a position farther from the lens to obtain a clear image.