Question

A lens of focal length 20 cm in air is made of glass with a refractive index of 1.6. What is its focal length when it is immersed in a liquid of refractive index 1.8?

• A. -36 cm
• B. -72 cm
• C. -60 cm
• D. -108 cm

Hint:

The focal length of a lens in a different medium can be calculated using the formula \( \frac{1}{f_{\text{medium}}} = \left( \frac{n_{\text{lens}}}{n_{\text{medium}}} \right) \times \frac{1}{f_{\text{air}}} \).

Answer 1

The Correct Option is A

The focal length of a lens in a medium is given by the formula: \[ \frac{1}{f_{\text{medium}}} = \left( \frac{n_{\text{lens}}}{n_{\text{medium}}} \right) \times \frac{1}{f_{\text{air}}} \] Where \( n_{\text{lens}} \) is the refractive index of the lens material, \( n_{\text{medium}} \) is the refractive index of the surrounding medium, and \( f_{\text{air}} \) is the focal length of the lens in air. Given: - \( f_{\text{air}} = 20 \, \text{cm} \) - \( n_{\text{lens}} = 1.6 \) - \( n_{\text{medium}} = 1.8 \) Substituting these values into the formula: \[ \frac{1}{f_{\text{medium}}} = \left( \frac{1.6}{1.8} \right) \times \frac{1}{20} \] \[ f_{\text{medium}} = \frac{1}{\left( \frac{1.6}{1.8} \right) \times \frac{1}{20}} = -36 \, \text{cm} \] Thus, the focal length of the lens when immersed in the liquid is \( -36 \, \text{cm} \). Therefore, the correct answer is (1) -36 cm.