Question

A beam of light coming parallel to the principal axis of a convex lens \( L_1 \) of focal length 16 cm is incident on it. Another convex lens \( L_2 \) of focal length 12 cm is placed coaxially at a distance 40 cm from \( L_1 \). The nature and distance of the final image from \( L_2 \) will be:

• A. Real, 24 cm
• B. Virtual, 12 cm
• C. Real, 32 cm
• D. Virtual, 18 cm

Hint:

When a convex lens forms an image at its focal point, it acts as an object for the next lens, and the final image position is determined using the lens equation.

Answer 1

The Correct Option is A

Image Formation Using Two Convex Lenses
- The first lens \( L_1 \) forms an image of an object at infinity at its focal point: \[ u_1 = \infty, \quad f_1 = 16 \text{ cm} \] \[ v_1 = f_1 = 16 \text{ cm} \] - This image acts as the object for the second convex lens \( L_2 \), placed 40 cm away: \[ u_2 = 40 - 16 = 24 \text{ cm}, \quad f_2 = 12 \text{ cm} \] Using the lens formula: \[ \frac{1}{v_2} - \frac{1}{u_2} = \frac{1}{f_2} \] \[ \frac{1}{v_2} - \frac{1}{24} = \frac{1}{12} \] \[ \frac{1}{v_2} = \frac{1}{12} + \frac{1}{24} = \frac{2}{24} + \frac{1}{24} = \frac{3}{24} \] \[ v_2 = 24 \text{ cm} \] - The positive value indicates a real image formed 24 cm from \( L_2 \). Thus, the correct answer is (A) Real, 24 cm.