Question

A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

• A. -160 cm
• B. 160 cm
• C. 16 cm
• D. -16 cm

Answer 1

The Correct Option is A

To determine the focal length of a biconvex lens submerged in a liquid, the lens maker's formula is applied, accounting for the surrounding medium's refractive index.

The lens maker's formula is:

\[\frac{1}{f} = \left( \frac{n_{\text{lens}}}{n_{\text{medium}}} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]

Here are the steps:

1. With the lens in air, \(n_{\text{lens}} = 1.5\) and \(n_{\text{medium}} = 1.0\). The lens formula yields an initial focal length, \(f_{\text{air}}\), of 20 cm:
2. This expression is rearranged to solve for \(\frac{1}{R_1} - \frac{1}{R_2}\):
3. When the lens is placed in a liquid with \(n_{\text{medium}} = 1.6\), the lens maker's formula is used again:
4. Substitute \(\frac{1}{R_1} - \frac{1}{R_2} = \frac{1}{10 \text{ cm}}\):
5. Simplify the equation:
6. Invert to find the focal length:

Consequently, the focal length of the lens in a liquid with a refractive index of 1.6 is -160 cm.