Question

The speed of light in glass is 2×10^8m\s if the speed of light in vacum be 3×10^8m/s, calculate the refractive index of glass

Answer 1

$\bigstar$Answer:

$\star$Given:

speed of light in glass (v) = 2 × 10⁸ m/s

Speed of light in vacuum (c) = 3.0 x 10⁸ m/s

$\star$To Find:

Refractive index of glass

$\star$Solution:

We know that,

Refractive index (μ) = velocity in vacuum/velocity in medium

The formula to be used here is,

$\red{\boxed{\boxed{\sf \mu = \dfrac{c}{v} }}}$

Given that,

c = 3.0 x 10⁸ m/s

v = 2 × 10⁸ m/s

Substituting the above values in the given formula,

We get,

$\sf \implies \mu = \dfrac{3 \times 10^8}{2 \times 10^8}$

$\sf \implies \mu = \dfrac{3}{2}$

$\implies \rm \mu = 1.5$

$\pink{\boxed{\boxed{\rm \mu = 1.5}}}$

Hence,

Refractive index of glass is 1.5

Answer 2

$\textbf{\huge\underline{\underline\red{solution} : - }} \\ \\ \textit{ \tt{The refractive index of a medium }} \\ \textit{ \tt{can be calculated using the }}\\ \textit{ \tt{following formula:}}\\ \textit{ \tt{</p><p></p><p> \red{ => n }}} \tt \red{= \frac{c}{v} }\\ \textit{ \tt{where}}\\ \textit{ \tt{ \red{n }is the refractive index of }}\\ \textit{ \tt{the medium}}.\\ \textit{ \tt{ \red{c }is the velocity of light }}\\ \textit{ \tt{in vacuum.}} \tt \purple{( 3 × {10}^{8} m/s)}\\ \textit{ \tt{</p><p></p><p> \red{v} is the velocity of light }}\\ \textit{ \tt{in the medium.}} \\ \\ \tt \underline\red{given } : - </p><p> \\ \\ \tt \red{c } \: of \: vacuum = 3 × {10}^{8} m/s \\ \tt \red{v} \: of \: glass = 2× {10}^{8} m/s \\ \tt \red{n} \: is \: refractive \: index = \: ? \\ \\ \tt \purple {by \: formula} \\ \tt \red{ = > n = \frac{c}{v } } \\ \\ \tt \purple{= > n = \frac{ 3 × \cancel{{10}^{8}} }{ 2 × \cancel{{10}^{8}} } = \frac{3}{2} = 1.5} \\ \\ \sf \blue {hence \: refractive \: index \: of \: glass \red{ \: n = \purple{1.5} }}$