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 find the location of the final image formed due to the combination of a convex lens and a plane mirror.

1. First, we will find the image distance formed by the convex lens using the lens formula: \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\) where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance. 
2. Given:
   • Focal length, \(f = 30 \, \text{cm}\)
   • Object distance, \(u = -60 \, \text{cm}\) (since the object is on the left side of the lens, we take it as negative)
3. Substituting in the lens formula: \(\frac{1}{30} = \frac{1}{v} + \frac{1}{60}\)
4. Simplifying: \(\frac{1}{v} = \frac{1}{30} - \frac{1}{60}\)
   \(\frac{1}{v} = \frac{2 - 1}{60}\)
   \(\frac{1}{v} = \frac{1}{60}\)
   \(v = 60 \, \text{cm}\)
5. The image is formed 60 cm on the right side of the lens, making it a real image.
6. The plane mirror is 40 cm from the lens on the right, so the real image formed by the lens is \((60 \, \text{cm} - 40 \, \text{cm}) = 20 \, \text{cm}\) in front of the mirror.
7. Since the image acts as an object for the mirror, and it is 20 cm in front of it, the mirror will form a virtual image at the same distance on the other side (behind the mirror).
8. Therefore, the final virtual image is formed 20 cm from the plane mirror, behind it.

The correct answer is: 20 cm from the plane mirror, it would be a virtual image.