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 ascertain the influence of refractive index \(\mu\) on lens power \(P\), we apply the lens maker's formula:

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

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

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

Substituting the lens maker's formula for \(\frac{1}{f}\) yields:

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

This equation indicates that when \(R_1\) and \(R_2\) are constant, \(P\) is directly proportional to \((\mu - 1)\).

Therefore, the relationship is \(P \propto (\mu - 1)\).