Question

A double convex lens of glass has both faces of the same radius of curvature 17 cm. Find its focal length if it is immersed in water. The refractive indices of glass and water are 1.5 and 1.33 respectively.

Hint:

The focal length of a lens changes when immersed in a medium other than air due to the change in the relative refractive index.

Answer 1

The focal length \( f \) of a lens in a medium is given by the lens maker's formula:\[ \frac{1}{f} = (n_{\text{lens}} - n_{\text{medium}}) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] For a double convex lens, \( R_1 = 17 \, \text{cm} \) and \( R_2 = -17 \, \text{cm} \). The refractive index of glass \( n_{\text{lens}} = 1.5 \) and water \( n_{\text{medium}} = 1.33 \). Substituting these values: \[ \frac{1}{f} = (1.5 - 1.33) \left( \frac{1}{17} - \frac{1}{-17} \right) \] \[ \frac{1}{f} = 0.17 \left( \frac{2}{17} \right) = 0.17 \times \frac{2}{17} = 0.02 \, \text{cm}^{-1} \] \[ f = \frac{1}{0.02} = 50 \, \text{cm} \] Thus, the focal length of the lens in water is \( 50 \, \text{cm} \).