Both radii of curvature of a convex lens are 20 cm and the refractive index of the material of the lens is 1.5. Rays parallel to the principal axis of the lens will converge at a distance from the lens of
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 cm
Rays parallel to the principal axis converge at the principal focus, so the distance asked is the focal length. It follows from the lens maker’s formula. With the Cartesian sign convention, the two faces of the convex lens have \( R_1=+20\,\mathrm{cm} \) and \( R_2=-20\,\mathrm{cm} \).
\( \begin{aligned} \frac{1}{f} &= (n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \\ &= (1.5-1)\left(\frac{1}{20}+\frac{1}{20}\right)\,\mathrm{cm^{-1}} \\ &= 0.5\times\frac{1}{10}\,\mathrm{cm^{-1}} \\ &= \frac{1}{20}\,\mathrm{cm^{-1}} \end{aligned} \)
\( f=20\,\mathrm{cm} \)
Therefore, the parallel rays converge 20 cm from the lens.