The light from a point source placed in air is incident on a convex spherical glass surface of radius of curvature 30 cm. The refractive index of the glass is 1.5. The distance of light source from the glass surface is 120 cm. The distance of the image formed from the glass surface is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 180 cm
For refraction at a single spherical surface,
\( \displaystyle \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \)
Take the direction of the incident light as positive (sign convention). The light travels from air (\( n_1 = 1 \)) into glass (\( n_2 = 1.5 \)), the surface is convex towards the source so \( R = +30\,\mathrm{cm} \), and the object is on the left, so \( u = -120\,\mathrm{cm} \).
\( \displaystyle \frac{1.5}{v} - \frac{1}{-120} = \frac{1.5 - 1}{30} \)
\( \displaystyle \frac{1.5}{v} = \frac{1}{60} - \frac{1}{120} = \frac{1}{120} \)
\( \displaystyle v = 1.5 \times 120 = 180\,\mathrm{cm} \)
The positive sign means the image is real and formed in the glass, 180 cm from the surface.
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Refraction at a Spherical Surface – …
