Question

A plano-convex lens is made from glass of refractive index \(1.5\). The radius of curvature of its curved surface is \(R\). Its focal length is

• A. \(1.5R\)
• B. \(2R\)
• C. \(R\)
• D. \(\dfrac{R}{2}\)

Hint:

For a plano-convex lens in air, focal length depends only on the curved surface radius and refractive index.

Answer 1

The Correct Option is B

Step 1: Use the lens maker’s formula.
For a thin lens in air,
\[ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
Step 2: Identify radii of curvature.
For a plano-convex lens, one surface is plane, so
\[ R_1 = R,\quad R_2 = \infty \]
Step 3: Substitute values.
\[ \frac{1}{f} = (1.5 - 1)\left(\frac{1}{R} - 0\right) = \frac{0.5}{R} \]
Step 4: Calculate focal length.
\[ f = 2R \]
Step 5: Conclusion.
The focal length of the plano-convex lens is \(2R\).