Question

the frequency of a light ray in a material is 2×10^4 and wavelength is 5000A°.The refractive index of material will be​

Answer 1

Given:

Frequency of a light wave = 2 × 10⁴ Hz

Wavelength = 5000 Å

Refractive index of material:

$\boxed{\sf{u = \frac{Velocity \: of \: light \: in \: vaccum}{Velocity \: of \: light \: in \: medium}}}$

That is:

$\boxed{\sf{u = \frac{c}{v}}}$

Thus,

By using: $\boxed{\sf{v = n\lambda}}$

$\implies$ n = 2 x 10⁴ Hz

$\implies$ λ = 5000 Å = $\sf{5 \times 10^{-13}}$

So:

$\sf{v = 2 \times 10^4 \times 5 \times 10^{-13}}$

$\sf{v = 10 \times 10^{-9}}$

$\sf{v = 10^{-8}}$

Refractive index of the material:

$\boxed{\sf{\mu=\frac{c}{v}}}$

$\implies$ $\sf{3 \times 10^{8} / \:10^{-8}}$

$\implies$ $\sf{3 \times 10^{16}}$

Thus:

The refractive index of material: $\sf{3 \times 10^{16}}$

Answer 2

Answer:-

Refractive index of medium = $\mu = 3$

Given :-

Frequency = 2 × 10¹⁴

Wavelength = $5\times 10^{-7} \dot{A}$

To find :-

The refractive index of that medium.

Solution:-

• We know that the wavelength, velocity and frequency is related by formula.

→$\boxed {V = n\lambda }$

• put the given values,

→$V = 2 \times 10^{14} \times 5 \times 10^{-7}$

→ $V = 10 \times 10^{14-7}$

→$V = 10 \times 10^{7}$

→$V = 10^{8} m/s$

→$\text{Refractive index} = \dfrac{\text{Speed of light in medium}}{\text{Speed of light in vaccum}}$

→$\mu = \dfrac{V}{C}$

• Put the given values,

→$\mu = \dfrac{3 \times 10^8}{10^{8} }$

→$\mu = 3$

hence,

Refractive index of medium will be

$\mu = 3$

Note :- you have written wrong frequency it is 2 × 10¹⁴