Question

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of

• A. 20 cm from the plane mirror, it would be a virtual image.
• B. 20 cm from the lens, it would be a real image
• C. 30 cm from the lens, it would be a real image.
• D. 30 cm from the plane mirror, it would be a virtual image.

Answer 1

The Correct Option is A

To solve this problem, we need to determine where the final image will be formed when a plane mirror is added to a setup with a convex lens.

Step-by-Step Solution:

1. Finding the Image Formed by the Convex Lens:
   According to the lens formula: \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\) where:
   • \(f = 30 \, \text{cm}\) (focal length of the lens)
   • \(u = -60 \, \text{cm}\) (object distance; negative as per sign convention)
2. Incorporating the Plane Mirror:
   The plane mirror is placed at a distance of 40 cm from the lens. Since the image formed by the lens is at 60 cm from the lens, it means the image is 20 cm behind the plane mirror (60 cm - 40 cm = 20 cm).
   A plane mirror will form an image at the same distance behind it as the object is in front. Therefore, the image formed by the lens will act as an object for the mirror, and a virtual image will be formed 20 cm in front of the mirror.

Conclusion:

The final image will be located 20 cm from the plane mirror, and it will be a virtual image.