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: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]. Given \( f = 20 \, \text{cm} \) (focal length) and \( u = -40 \, \text{cm} \) (object distance, negative as it's on the incident light side), we calculate the image distance \( v \). The formula rearranged for \( v \) is: \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]. Substituting values: \[ \frac{1}{v} = \frac{1}{20} + \frac{1}{-40} = \frac{1}{20} - \frac{1}{40} = \frac{2 - 1}{40} = \frac{1}{40} \]. Therefore, \( v = 40 \, \text{cm} \). A positive \( v \) indicates the image forms on the side opposite the object. The image is located 40 cm from the lens, on the opposite side of the object.