Question

The refractive index of diamond is 2.42 and that of glass is 1.5 find the ratio of velocity of light in glass with the velocity of light in diamond?plz include all the steps its utgent fast!!!!

Answer 1

▶ SOLUTION :

Given :

▪ Refractive index of diamond = 2.42

▪ Refractive index of glass = 1.5

To Find :

▪ Ratio of velocity of light in glass to the velocity of light diamond.

Concept :

✏ Refractive index of a medium is defined as the ratio of velocity of light in vacuum to the velocity of light in medium.

✏ Refractive index is an unitless quantity.

Calculation :

$\implies\bf\:n=\dfrac{velocity\:of\:light\:in\:vacuum}{velocity\:of\:light\:in\:medium}\\ \\ \implies\sf\:\dfrac{n_{glass}}{n_{diamond}}=\dfrac{v_{diamond}}{v_{glass}}\\ \\ \implies\sf\:\dfrac{v_{diamond}}{v_{glass}}=\dfrac{1.5}{2.42}\\ \\ \implies\boxed{\bf{\purple{v_{glass}:v_{diamond}=1.61:1}}}$

Answer 2

Given:

Refractive index of Diamond= 2.42

Refractive index of Glass= 1.5

To Find:

Ratio of velocity of light in glass to the velocity of light in diamond

Solution:

We know that,

$\sf\pink{Refractive\:Index\:of\:Medium=\dfrac{Speed\:of\:light\:in\:Vacuum}{Speed\:of\:light\:in\:Medium}}$

Now,

For Glass

$\sf{Refractive\:Index\:of\:Glass=\dfrac{Speed\:of\:light\:in\:Vacuum}{Speed\:of\:light\:in\:Glass}}$

$\sf{1.5=\dfrac{c}{Speed\:of\:light\:in\:Glass}}$

where c= 3×10⁸ m/s

$\sf{Speed\:of\:light\:in\:Glass=\dfrac{c}{1.5}}---(1)$

For Diamond

$\sf{Refractive\:Index\:of\:Diamond=\dfrac{Speed\:of\:light\:in\:Vacuum}{Speed\:of\:light\:in\:Diamond}}$

$\sf{2.42=\dfrac{c}{Speed\:of\:light\:in\:Diamond}}$

where c= 3×10⁸ m/s

$\sf{Speed\:of\:light\:in\:Diamond=\dfrac{c}{2.42}}---(2)$

On diving (1) by (2), we get

$\longrightarrow\mathrm{\dfrac{Speed\:of\:light\:in\:Glass}{Speed\:of\:light\:in\:Diamond}=\dfrac{\dfrac{\cancel{c}}{1.5}}{\dfrac{\cancel{c}}{2.42}}}$

$\longrightarrow\mathrm{\dfrac{Speed\:of\:light\:in\:Glass}{Speed\:of\:light\:in\:Diamond}=\dfrac{2.42}{1.5}}$

$\longrightarrow\mathrm{\dfrac{Speed\:of\:light\:in\:Glass}{Speed\:of\:light\:in\:Diamond}=\dfrac{242}{150}}$

$\longrightarrow\mathrm{\dfrac{Speed\:of\:light\:in\:Glass}{Speed\:of\:light\:in\:Diamond}=\dfrac{121}{75}}$

Hence, the required ratio is 121/75 or 121:75 .