Question

The refractive index of water with respect to air is
q mu w and of glass with respect to air is a mu g. Express,
the refractive index of glass with respect to water.
give step by step explanation ​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Refractive index of water with respect to air = ${\sf _g\mu_w=}$
• Refractive index of glass with respect to air =${\sf _a\mu_g}$

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Refractive index of glass with respect to water =${\sf _w\mu_g}$

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$\color{darkblue}\underline{\underline{\sf Formula \: Used-}}$

$\color{violet}\bullet\underline{\boxed{\sf _a\mu_g × _g\mu_w × _w\mu_a = 1}}$

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$\color{darkblue}\underline{\underline{\sf Solution-}}$

We know that -

$\color{navy}\implies{\sf _a\mu_g = \dfrac{3}{2}}$

$\color{navy}\implies{\sf _w\mu_a=\dfrac{3}{4} }$

$\implies{\sf \therefore \: \: _a\mu_g×_g\mu_w×_w\mu_a=1}$

$\implies{\sf \dfrac{3}{2}×_g\mu_w×\dfrac{3}{4}=1}$

$\implies{\sf _g\mu_w=\dfrac{4×2}{3×3}}$

$\implies{\sf _g\mu_w=\dfrac{8}{9}}$

and

$\large\bullet\underline{\boxed{\sf _w\mu_g=\dfrac{1}{_g\mu_w}}}$

$\color{red}\implies{\sf _w\mu_g=\dfrac{9}{8}}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

The refractive index of glass with respect to water is $\color{red}{\sf \dfrac{9}{8}}$

Answer 2

Answer:

Refractive index of glass with respect to water is (9/8). Refractive index of glass with respect to air is (3/2).

Refractive index is not defined for one material with respect to another. Each material has its own refractive index. The refractive index of air is about 1.0003, and the index of water is about 1.333.

refractive index have no si units, since from the definition refractive index is the ratio of velocity of light in a material divided with velocity of light in vacuum. this is what is meant by "integral".