If in a plano-convex lens, the radius of the convex surface is 10 cm and the focal length is 30 cm. Then the refractive index of the material will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.33
The lens maker's formula links the focal length to the refractive index and the radii of the two surfaces. For a plano-convex lens the plane surface has \( R_2 = \infty \), so \( 1/R_2 = 0 \).
\( \displaystyle \frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = \frac{n - 1}{R_1} \)
\( R_1 = 10\,\mathrm{cm} \)
\( f = 30\,\mathrm{cm} \)
\( \displaystyle \frac{1}{30} = \frac{n - 1}{10} \;\Rightarrow\; n - 1 = \frac{10}{30} = \frac{1}{3} \)
\( \displaystyle n = 1 + \frac{1}{3} = 1.33 \)