Question

A point object is placed at a distance of 25 cm from a thin plano-convex lens of focal length 20 cm. The plane surface of the lens is now silvered. The image created by the system is at:

• A. 100 cm to the left of the system
• B. 100 cm to the right of the system
• C. 16.7 cm to the right of the system
• D. 16.7 cm to the left of the system

Hint:

For a silvered plano-convex lens, the lens acts as a concave mirror. Use the mirror formula to find the image distance.

Answer 1

The Correct Option is D

Since the lens is silvered, it will act as a concave mirror, and the focal length \( f \) becomes negative. The focal length of the mirror is \( f = -20 \, \text{cm} \). Using the mirror formula: \[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \] where: - \( f = -20 \, \text{cm} \), - \( u = -25 \, \text{cm} \) (since the object is 25 cm from the mirror), - \( v \) is the image distance we need to find. Substitute the values: \[ \frac{1}{-20} = \frac{1}{-25} + \frac{1}{v} \] Solving for \( v \), we get: \[ \frac{1}{v} = \frac{1}{-20} - \frac{1}{-25} = -\frac{1}{100} \] Thus, \[ v = -100 \, \text{cm} \] This means the image is formed 100 cm to the left of the system.