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Derive an expression for refraction at a single (convex) spherical surface, i.e. a relation between…

Physics20205 marksShort answer
(i)[4.0]
Derive an expression for refraction at a single (convex) spherical surface, i.e. a relation between $u$, $v$, $R$, $n_1$ (rarer medium) and $n_2$ (denser medium), where the terms have their usual meaning.

Given: A spherical convex surface separating a rarer medium of refractive index $n_1$ from a denser medium of refractive index $n_2$

To show: $\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$

(ii)[1.0]
Name the phenomenon due to which the sun appears reddish at sunset.

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Ray Optics and Optical Instruments

From ISC 2020 Physics Paper 1, question 21(a).