Question

A light beam with a 70° angle of incidence travels through a medium with an index of refraction of 1.8. The light enters a second medium and has an angle of refraction of 37°. What is the index of refraction of the second medium?

Answer 1

Answer:

Explanation:

For refraction , the formula is

sin i / sin r = μ₂ / μ₁

where light is travelling from medium 1 to 2 having refractive index of μ₁ and μ₂ . Angle of incidence in medium 1 is i and angle of refraction in medium 2 is r .

Here i = 70°, r = 37°

μ₁ = 1.8 ,μ₂ = ?

sin70 / sin 37 = μ₂ / 1.8

.939 / .602 = μ₂ / 1.8

1.56 =  μ₂ / 1.8

μ₂ = 2.81 .

Answer 2

The value of refraction index for the second medium will be  $\mu_2=2.16$

What will be the refractive index?

Every material has a different refractive index. The refracted index of any material shows that the light is refracted by how much angle.

So like for water its value will be different also for glass its value will be different.

Now it is given in the question that

Angle of incidence $i=70^o$

Refractive index of the first medium $\mu_1=1.8$

Angle of refraction $r=37^o$

Now from snells law

$\dfrac{Sin \ i}{Sin \ r} = \dfrac{\mu_2}{\mu_1}$

$\dfrac{Sin70}{Sin37} = \dfrac{\mu_2}{1.8}$

$\mu_2= \dfrac{Sin70\times1.8}{Sin37}$

$\mu_2=2.16$

Thus the value of the refraction index for the second medium will be  $\mu_2=2.16$

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