Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The relation \(\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\) for refraction at a spherical surface holds for a convex surface but not for a concave surface.
Reason (R): A very small part of a spherical surface can be taken as plane, so the laws of refraction can be applied at every point of the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) is not correct but (R) is correct.
Assertion (A) The relation \(\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\) for refraction at a spherical surface holds for a convex surface but not for a concave surface. — False. This relation holds for any curved spherical surface. For a concave surface, the centre of curvature is on the side of the incident light. So \(R\) is put in as a negative value, as the Cartesian sign convention requires.
Reason (R) A very small part of a spherical surface can be taken as plane, so the laws of refraction can be applied at every point of the surface. — True. A tiny part of the curved surface behaves like a flat surface. So Snell’s law can be used where each ray meets it. The normal at that point passes through the centre of curvature.
NCERT (2026-27):
Refraction at Spherical Surfaces and by Lenses – “… An infinitesimal part of a spherical surface can be regarded as planar and the same laws of refraction can be applied at every point on the surface. …”
Refraction at a spherical surface – “… Substituting these in … we get”
\( \displaystyle \frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R} \qquad (9.16) \)
“Equation (9.16) gives us a relation between object and image distance in terms of refractive index of the medium and the radius of curvature of the curved spherical surface. It holds for any curved spherical surface.”