Question

Q. Find angle of re fraction
45
n=1
n=√2​

Answer 1

Given:

Refractive index of first medium, n₁= 1

Refractive index of second medium, n₂ = √2

Angle of incidence, i= 45°

To Find:

Angle of refraction

Solution:

We know that,

• According to Snell's Law

$\pink{\boxed{\bf{\dfrac{sin\:i}{sin\:r}=\dfrac{\mu_{2}}{\mu_{1}}}}}$

where,

i is angle of incidence

r is angle of refraction

μ₁ is refractive index of medium where incident ray is present

μ₂ is refractive index of medium where refracted ray is present

$\rule{190}{1}$

Let the angle of refraction be r

On using Snell's law ,we get

$\longrightarrow\rm{\dfrac{sin\:i}{sin\:r}=\dfrac{n_{2}}{n_{1}}}$

$\longrightarrow\rm{\dfrac{sin\:45^{\circ}}{sin\:r}=\dfrac{\sqrt{2}}{1}}$

$\longrightarrow\rm{\dfrac{\dfrac{1}{\sqrt{2}}}{sin\:r}=\sqrt{2}}$

$\longrightarrow\rm{\dfrac{1}{\sqrt{2}\:sin\:r}=\sqrt{2}}$

$\longrightarrow\rm{\dfrac{1}{\:sin\:r}=\sqrt{2}\times\sqrt{2}}$

$\longrightarrow\rm{\dfrac{1}{\:sin\:r}=2}$

$\longrightarrow\rm{sin\:r=\dfrac{1}{2}}$

$\longrightarrow\rm{r=sin^{-1}\bigg(\dfrac{1}{2}\bigg)}$

$\longrightarrow\rm\green{r=30^{\circ}}$

Hence, the angle of refraction is 30°.