Question

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the center. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

• A. -20 cm
• B. -25 cm
• C. -50 cm
• D. 50 cm

Hint:

When combining lenses with different refractive indices, use the lens maker's formula to find the effective focal length.

Answer 1

The Correct Option is C

The focal length \( f \) of a plano-convex lens is given by: \[ \frac{1}{f} = \left( \frac{n - 1}{R} \right) \] For the combination of lenses, we can calculate the effective focal length by considering the refractive index of the lenses and the intervening medium (oil). Using the lens maker's formula and the refractive index values, we find that the effective focal length of the combination is -50 cm. Hence, the correct answer is (c).