Question

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$\sf \large \green{Answer \: This!}$
$\small \sf{What \: is \: the \: speed \: of \: light \: in \: a \: medium}$
$\small \sf{whose \: refractive \: index \: is \: \frac{4}{3}, \: if \: the \: speed \: of \: }$
$\small \sf{light \: in \: air \: is \: 3 \times {10}^{8}m \: {s}^{ - 1}?}$






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Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given:

$\sf \implies Refractive \ \: Index ( \mu) = \dfrac{4}{3}$

$\sf \implies c = 3 \times {10}^{8} \: m/s$

Note: c means the speed of light in air.

We know that:

$\sf \implies \mu = \dfrac{Speed \: of \: light \: in \: air \: (c) }{Speed \: of \: light \: in \: medium (V) }$

Substitute the values in the formula. We get:

$\sf \implies \dfrac{4}{3} = \dfrac{3 \times {10}^{8} }{V}$

$\sf \implies V = \dfrac{3 \times 3 \times {10}^{8} }{4}$

$\sf \implies V = \dfrac{9 \times {10}^{8} }{4}$

$\sf \implies V = \dfrac{9}{4} \times {10}^{8} \: m/s$

$\sf \implies V = 2.25 \times {10}^{8} \: m/s$

★ So, the speed of light in that medium will be – 2.25 × 10⁸ m/s.

$\texttt{\textsf{\large{\underline{Know More}:}}}$

Laws of refraction:

1. The incident ray, the refracted ray and the normal at the point of incidence, all lie in the same plane.

2. The ratio of the sine of angle of incidence to the sin of angle of refraction is constant for a pair of media.

$\sf \mapsto \dfrac{sin(i)}{sin(r)} = constant(_{1} \mu_{2})$