Question

A convex lens has focal length 20 cm. An object is placed at a distance of 40 cm from the lens. What is the position of the image formed?

• A. 40 cm on the opposite side
• B. 20 cm on the same side
• C. 20 cm on the opposite side
• D. 40 cm on the same side

Hint:

For a convex lens, if the object is placed beyond the focal length, the image formed is real, inverted, and on the opposite side of the object.

Answer 1

The Correct Option is D

The lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where: - \( f = 20 \, \text{cm} \) (focal length of the lens) - \( u = -40 \, \text{cm} \) (object distance; negative because the object is on the same side as the incoming light) We need to find the image distance \( v \). Rearranging the lens formula: \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \] Substituting the values: \[ \frac{1}{v} = \frac{1}{20} + \frac{1}{-40} = \frac{1}{20} - \frac{1}{40} = \frac{2 - 1}{40} = \frac{1}{40} \] Thus, \[ v = 40 \, \text{cm} \] Since \( v \) is positive, the image is formed on the opposite side of the object. The position of the image is 40 cm on the opposite side.