Question

For fixed values of radii of curvature of lens, power of the lens will be ____.
Fill in the blank with the correct answer from the options given below

• A. \(P \propto (\mu - 1)\)
• B. \(P \propto \mu^2\)
• C. \(P \propto \frac{1}{\mu}\)
• D. \(P \propto \mu^{-2}\)

Answer 1

The Correct Option is A

To determine how the power \(P\) of a lens is affected by the refractive index \(\mu\), we need to use the lens maker's formula: 

\(\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\)

where \(f\) is the focal length of the lens, \(\mu\) is the refractive index of the lens material, and \(R_1\) and \(R_2\) are the radii of curvature of the lens surfaces. The power of the lens \(P\) is defined as the reciprocal of the focal length:

\(P = \frac{1}{f}\)

Upon substituting the expression for \(\frac{1}{f}\) from the lens maker's formula, we get:

\(P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\)

This equation shows that for fixed values of the radii of curvature \(R_1\) and \(R_2\), the power \(P\) is directly proportional to \((\mu - 1)\).

Thus, the correct answer is \(P \propto (\mu - 1)\).