Question

ray of light travelling in air is incident on the plane of a transparent medium. The angle of incident is 450 and that of refraction is 300. Find the refractive index of the medium​

Answer 1

Given :

• The angle of incident =45 degree

• The angle of refraction =30 degree

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To Find :

• The refractive index of the medium =?

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Formula :

$\\ \red\bigstar\boxed{\sf{ \dfrac{\mu_{2}}{\mu_{1}}=\dfrac{sini}{sinr}}}$

Solution:

>> Snell law of refraction gives the relation between the incident and reflected light at the interface of two media , which is given by

$\\ \green\bigstar\boxed{\sf{\dfrac{\mu_{2}}{\mu_{1}}=\dfrac{sini}{sinr}}}$

• The initial medium is air . Then $\sf{\mu_{1}=1}$

Given,

$\\ \rm{angle \: of \: incidence =45\degree}$

$\\ \rm{angle \: of \: refraction =30\degree}$

By Snell's Rule :

$\\ \implies\sf{\dfrac{\mu_{2}}{\mu_{1}}=\dfrac{sini}{sinr}}$

$\\ \implies\sf{\mu_{2}=\mu_{1} \times \dfrac{sini}{sinr}}$

$\\ \implies\sf{\mu_{2}=1\times \dfrac{sin45\degree}{sin30\degree}}$

$\\ \implies\boxed{\sf{\mu_{2}=\sqrt{2}}}$