Question

What is absolute refractive index? If the refractive indices of glass and water are 3/2 and 4/3. Determine the ratio of speed of light in glass to water.

Answer 1

Answer:

1 ) refractive index is actually a relative quantity as every substances refractive index is compared with refractive index of light in vaccum and assuming refractive index of light in vaccum as 1

so actually absolute refractive is defined as speed of light in vaccum / speed of light in the given medium

2 ) actually refrctive index is inversly propotional to speed of light in that substance

so velocity is also inversely proportional to refractive index

so v1 / v2 = mu2 / mu1 (where mu represent refractive index )

so by this formula your answer is

8 / 9

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Answer 2

Given :

▪ Refractive index of glass = 3/2

▪ Refractive index of water = 4/3

To Find :

▪ Ratio of speed of light in glass to water.

$\bigstar\:\underline{\boxed{\bf{\green{Refractive}\:\gray{Index}\red{:}}}}$

→ Refractive index of a medium is defined as the factor by which speed of light reduces as compared to the speed of light in vacuum.

Mathematically,

$\bigstar\:\underline{\boxed{\bf{\purple{n=\dfrac{c}{v}=\dfrac{speed\:of\:light\:in\:vacuum}{speed\:of\:light\:in\:medium}}}}}$

→ More (less) refractive index implies less (more) speed of light in that medium, which therefore is called denser (rarer) medium.

Calculation :

$\dashrightarrow\sf\:\dfrac{n_w}{n_g}=\dfrac{\frac{c}{v_w}}{\frac{c}{v_g}}\\ \\ \dashrightarrow\sf\:\dfrac{v_g}{v_w}=\dfrac{n_w}{n_g}\\ \\ \dashrightarrow\sf\:\dfrac{v_g}{v_w}=\dfrac{\frac{4}{3}}{\frac{3}{2}}\\ \\ \dashrightarrow\underline{\boxed{\bf{\pink{v_g:v_w=8:9}}}}\:\orange{\bigstar}$