Question

A convex lens of focal length 10 cm is placed coaxially at a distance of 4 cm to the right of another convex lens of focal length 16 cm. If an object is placed at a distance of 8 cm to the left of the convex lens of focal length 16 cm, then the distance of the final image from the object is:

• A. 28 cm
• B. 40 cm
• C. 36 cm
• D. 32 cm

Hint:

When working with compound lenses, the image formed by the first acts as the object for the second, requiring careful tracking of distances relative to each lens.

Answer 1

The Correct Option is B

For the first lens with a focal length of 16 cm, the image is calculated using the lens formula. The object distance is \( -8 \, \text{cm} \), leading to a virtual image positioned at \( -16 \, \text{cm} \) relative to the first lens. This virtual image acts as the object for the second lens, positioned 4 cm to the right, making its effective object distance \( -12 \, \text{cm} \). The second lens, having a focal length of 10 cm, forms the final image 60 cm to its right. Thus, the total distance from the original object to the final image is \( 8 \, \text{cm} + 60 \, \text{cm} = 68 \, \text{cm} \).