The Equation of Refraction at a Spherical Surface is μ 2 ν − μ 1 μ = μ 2 − μ 1 R - Physics

Sum

The equation of refraction at a spherical surface is $\frac{\mu_2}{\nu} - \frac{\mu_1}{\mu} = \frac{\mu_2 - \mu_1}{R}$
Taking $R = \infty$ show that this equation leads to the equation
$\frac{\text{ Real depth }}{\text{ Apparent depth }} = \frac{\mu_2}{\mu_1}$
for refraction at a plane surface.

Solution

Proof:

$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$

$Now R = \infty$

$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{\infty}$

$\frac{\mu_2}{v} - \frac{\mu_1}{u} = 0$

$\frac{\mu_2}{v} = \frac{\mu_1}{u}$

$\frac{\mu_1}{\mu_2} = \frac{u}{v}$

$But \frac{u}{v} = \frac{\text{ Real depth/height}}{\text{ Apparent depth/height}}$

$\therefore \frac{\text{ Real depth }/height}{\text{ Apparent depth/height }} = \frac{\mu_1}{\mu_2}$

Concept: Refraction at Spherical Surfaces and by Lenses - Refraction at Spherical Surfaces
Is there an error in this question or solution?

APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 18 Geometrical Optics
Short Answers | Q 11 | Page 410