Question

A biconvex lens (\(R_1 = R_2 = 20\,\text{cm}\)) has focal length equal to the focal length of a concave mirror. The radius of curvature of the concave mirror is (\(\mu\) of glass lens = 1.5)

• A. \(-40\,\text{cm}\)
• B. \(-20\,\text{cm}\)
• C. \(40\,\text{cm}\)
• D. \(20\,\text{cm}\)

Hint:

Always apply correct sign convention: concave mirror has negative radius of curvature.

Answer 1

The Correct Option is A

Step 1: Use lens maker’s formula.
\[ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \] For a biconvex lens, \(R_1 = +20\,\text{cm}\), \(R_2 = -20\,\text{cm}\).

Step 2: Substitute values.
\[ \frac{1}{f} = (1.5 - 1)\left(\frac{1}{20} - \left(-\frac{1}{20}\right)\right) = 0.5 \times \frac{2}{20} = \frac{1}{20} \] \[ f_{\text{lens}} = 20\,\text{cm} \]

Step 3: Use mirror formula.
For a concave mirror, \[ f = \frac{R}{2} \Rightarrow R = 2f = 40\,\text{cm} \] By sign convention for concave mirror, \(R\) is negative.

Step 4: Final result.
\[ R = -40\,\text{cm} \]