Question

An object O is placed in front of two thin coaxial convex lenses A and B of focal lengths 24 cm and 9 cm respectively. The object is 6 cm to the left of lens A. If the final image is formed 18 cm to the right of lens B, find the separation between the lenses. (Lens A is placed left of lens B)

• A. 5 cm
• B. 10 cm
• C. 8 cm
• D. 12 cm

Hint:

For multi-lens systems, treat the image of first lens as object for second lens carefully with sign convention.

Answer 1

The Correct Option is B

Step 1: Image from lens A.
1/f_A = 1/v_A - 1/u_A; 1/24 = 1/v_A + 1/6 → 1/v_A = 1/24 - 1/6 = -3/24 → v_A = -8 cm.

Step 2: Object distance for lens B.
With separation d, u_B = -(d - 8).

Step 3: Lens B formula.
1/9 = 1/18 - 1/u_B.

Step 4: Determining u_B.
1/u_B = 1/18 - 1/9 = -1/18 → u_B = -18 cm.

Step 5: Finding separation.
-(d - 8) = -18 → d = 10 cm.

Step 6: Conclusion.
The lenses are separated by 10 cm.