Question

A thin lens of glass of refractive index 1.5 has focal length 24 cm in air. It is now immersed in a liquid of refractive index \( \frac{9}{8} \). Its new focal length is:

• A. 72 cm
• B. 54 cm
• C. 36 cm
• D. 18 cm

Hint:

When a lens is immersed in a medium with a different refractive index, its focal length changes according to the relative refractive indices of the lens and the medium.

Answer 1

The Correct Option is C

Step 1: Formula for Focal Length.
The focal length \( f \) of a lens is given by: \[ \frac{1}{f} = \left( \frac{\mu - 1}{R} \right) \] where \( \mu \) is the refractive index of the lens material and \( R \) is the radius of curvature. In air, the refractive index of the lens is 1.5, and in the liquid, the effective refractive index is \( \frac{9}{8} \). The new focal length can be calculated by adjusting the refractive index, yielding a new value of 36 cm.
Step 2: Final Answer.
Thus, the new focal length of the lens is 36 cm.