Question

The refractive index of glass with respect to air is 3/2 and refractive index of water with respect to air is 4/3 . What will be the refractive index of glass with water .... Answer needed with steps

Answer 1

Given :

▪ Refractive index of glass wrt air = 3/2

▪ Refractive index of water wrt air = 4/3

To Find :

▪ Refractive index of glass wrt water.

Concept :

❇ 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.

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

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

❇ Refractive index of medium A wrt medium B is given by

$\bigstar\:\underline{\boxed{\bf{\blue{n_{AB}=\dfrac{n_A}{n_B}}}}}$

CalculaTion :

$\dashrightarrow\sf\:n_{gw}=\dfrac{n_{ga}}{n_{wa}}\\ \\ \dashrightarrow\sf\:n_{gw}=\dfrac{n_g}{\cancel{n_a}}\times \dfrac{\cancel{n_a}}{n_w}\\ \\ \dashrightarrow\sf\:n_{gw}=\dfrac{n_g}{n_w}=\dfrac{3\times 3}{2\times 4}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{n_{gw}=\dfrac{9}{8}}}}}\:\orange{\bigstar}$

☣ Extra Dose :

• Refractive index of medium is an unitless as well as dimensionless quantity.

Answer 2

Answer :

Refractive index of water wrt air (water n air)= 4/3

Refractive index of glass wrt air (glass n air) = 3/2

Refractive index of glass wrt water ( glass n water) = (glass n air)× (air n water) = (glass n air)× (1/water n air) = 4/3 × 2/3 = 8/9.

My above answer written by me was wrong. The correct answer is not 8/9 but rather 9/8.

Refractive index of water wrt air= 4/3

Refractive index of glass wrt to air = 3/2

Refractive index of air wrt water = 1/(refractive index of water wrt air) = 1/(4/3) = 3/4

Refractive index of glass wrt water = (Refractive index of glass wrt air) × (refractive index of air wrt water) = (3/2) × (3/4) = 9/8.

$\rule{200}{2}$