Question

The refractive index of air with respect to glass is 2/3 and the refractive index of water with respect to air is 4/3. If the speed of light in glass is 2×108 m/s. Find the speed of light (i) in air and (ii) water.

Answer 1

$\gray{\bigstar}\:\underline{\boxed{\mathbb{\large{\orange{ANSWER:}}}}}$

RI of air wrt glass $=$ 2/3

[Therefore, RI of glass wrt air will be 3/2]

RI of water wrt air $=$ 4/3

Speed of light in glass = 2×$10^8$ m/s

We have to find speed of light in air and water$.$

◈ What is Refractive index ?

Refractive index is defined as the ratio of speed of light in vacuum to the speed of light in medium.

Mathematically, n = c/v

☃ Let's calculate :

(✪) Case - A :

➝ $\sf{n_{g}=\dfrac{c}{v_{g}}}$

➝ $\sf{c=\dfrac{3}{2}\times 2\times 10^8}$

➝ $\boxed{\bf{c=3\times 10^8\:mps}}$

(✪) Case - B :

➝ $\sf{n_{w}=\dfrac{c}{v_{w}}}$

➝ $\sf{v_{w}=\dfrac{3\times 10^8}{\frac{4}{3}}}$

➝ $\boxed{\bf{v_{w}=2.25\times 10^8\:mps}}$