Question

The focal length of an equiconvex lens:

• A. Increases when the lens is dipped in water.
• B. Increases when the wavelength of incident light decreases.
• C. Increases with decrease in the radius of curvature of its surface.
• D. Decreases when the lens is cut into two identical parts along its principal axis.

Hint:

The focal length of a lens increases when placed in a medium with a refractive index closer to that of the lens material.

Answer 1

The Correct Option is A

Effect of Surrounding Medium on Focal Length
- The focal length of a lens is given by the lens maker’s formula: \[ \frac{1}{f} = (n_{\text{lens}} - n_{\text{medium}}) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where:
- \( n_{\text{lens}} \) = Refractive index of the lens material.
- \( n_{\text{medium}} \) = Refractive index of the surrounding medium.
- \( R_1, R_2 \) = Radii of curvature of the lens. Effect of Dipping the Lens in Water
- When the lens is in air, \( n_{\text{medium}} = 1 \).
- When dipped in water, \( n_{\text{medium}} \approx 1.33 \).
- Since the focal length is inversely proportional to \( (n_{\text{lens}} - n_{\text{medium}}) \), as \( n_{\text{medium}} \) increases, the focal length also increases. Thus, the correct answer is (A) The focal length increases when the lens is dipped in water.