Question

The refractive index of water is 1.33 and glycerine is 1.473. Calculate
refractive index of the glycerine with respect to water.​

Answer 1

Given :

Refractive index of water = 1.33

Refractive index of glycerine = 1.473

To Find :

Refractive index of glycerine with respect to water.

Solution :

❖ 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.

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

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

Refractive index of medium 1 with respect to medium 2 is given by, n₁₂ = n₁ / n₂

$\sf:\implies\:n_{gw}=\dfrac{n_g}{n_w}$

$\sf:\implies\:n_{gw}=\dfrac{1.473}{1.33}$

$:\implies\:\underline{\boxed{\bf{\gray{n_{gw}=1.11}}}}$

Answer 2

Given :

Refractive index of water = 1.33

Refractive index of glycerine = 1.473

To Find :

Refractive index of glycerine with respect to water.

Solution :

❖ 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.

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

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

Refractive index of medium 1 with respect to medium 2 is given by, n₁₂ = n₁ / n₂

$\sf:\implies\:n_{gw}=\dfrac{n_g}{n_w}$

$\sf:\implies\:n_{gw}=\dfrac{1.473}{1.33}$

$:\implies\:\underline{\boxed{\bf{\gray{n_{gw}=1.11}}}}$