Question

Find the ratio of the focal length of lens in air and that of lens when it is immersed in liquid. 
 

Hint:

The focal length of a lens changes when it is immersed in a medium due to the change in the relative refractive index.

Answer 1

The focal length of a lens in air is given by the lens formula: \[ \frac{1}{f_{\text{air}}} = \left( \mu - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right), \] where \( \mu \) is the refractive index of the material of the lens, and \( R_1 \) and \( R_2 \) are the radii of curvature of the lens. When the lens is immersed in a liquid of refractive index \( \mu_{\text{liquid}} \), the focal length is: \[ \frac{1}{f_{\text{liquid}}} = \left( \mu_{\text{lens}} - \mu_{\text{liquid}} \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right). \] The ratio of the focal lengths is: \[ \frac{f_{\text{air}}}{f_{\text{liquid}}} = \frac{\mu_{\text{lens}} - 1}{\mu_{\text{lens}} - \mu_{\text{liquid}}}. \]