Question

What is the focal length of a plano-convex lens if 'R' is the radius of curvature and ‘n’ is the refractive index?

• A. \(f=R\)
• B. \(f=\frac R2\)
• C. \(f=\frac {R}{n-1}\)
• D. \(f=\frac {n-1}{R}\)

Answer 1

The Correct Option is C

To solve the problem, we need to find the focal length of a plano-convex lens, where $R$ is the radius of curvature and $n$ is the refractive index.

1. Understanding the Lens Formula:
For a plano-convex lens, the focal length $f$ can be derived using the lens maker's formula. For a plano-convex lens, the formula is:

$ f = \frac{R}{n - 1} $

Where:
- $R$ is the radius of curvature of the curved surface.
- $n$ is the refractive index of the material of the lens.

2. Deriving the Formula:
This formula is used for a lens where one side is flat (plano) and the other side is curved (convex), and it gives the relationship between the radius of curvature and the refractive index in determining the focal length.

3. Final Answer:
The focal length of the plano-convex lens is $ \mathbf{f = \frac{R}{n - 1}} $.