Light from a point source in the air falls on a convex spherical glass surface having radius of curvature 20 cm and refractive index 1.5. The distance of the light source from the glass surface is 100 cm. The distance of the image from the glass surface is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 100\,\mathrm{cm} \)
Use the formula for refraction at a spherical surface, with the Cartesian sign convention: distances are measured from the pole, positive in the direction of the incident light.
\( \displaystyle \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \)
\( n_1 = 1 \text{ (air)},\ n_2 = 1.5 \)
\( u = -100\,\mathrm{cm} \)
\( R = +20\,\mathrm{cm} \text{ (surface convex towards the source)} \)
\( \displaystyle \frac{1.5}{v} - \frac{1}{-100} = \frac{1.5 - 1}{20} \)
\( \displaystyle \frac{1.5}{v} + 0.01 = 0.025 \;\Rightarrow\; \frac{1.5}{v} = 0.015 \)
\( \displaystyle v = +100\,\mathrm{cm} \)
The positive sign means a real image inside the glass, 100 cm from the surface.
Note: A similar question was also asked in CUET (UG) 2023 on 12-06-2023 (Slot 3).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Refraction at a Spherical Surface – …
