A double convex lens of refractive index 1.5 has a radius of curvature R each. The focal length of the lens is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $R$
Given:
Refractive index of lens, $\mu = 1.5$
Radii of curvature: $R_1 = R$, $R_2 = -R$ (for double convex lens)
Lens maker’s formula:
$\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$
Substitute values:
$\frac{1}{f} = (1.5 - 1)\left(\frac{1}{R} - \frac{1}{-R}\right)$
$\frac{1}{f} = 0.5 \left(\frac{1}{R} + \frac{1}{R}\right)$
$\frac{1}{f} = 0.5 \times \frac{2}{R}$
$\frac{1}{f} = \frac{1}{R}$
Final Answer: $f = R$