Question

calculate the angle of incidence if the angle of refraction is 30° in a medium of critical angle 45°​

Answer 1

The angle of incidence is $44.8^{\circ}$

Explanation:

The critical angle of a medium is given by the equation

$sin \theta_c = \frac{1}{n}$

where

$\theta_c$ is the critical angle

n is the index of refraction of the medium

Here we know that

$\theta_c$

So we can find the index of refraction of the medium:

$n=\frac{1}{sin \theta_c}=\frac{1}{sin 45}=1.41$

Now we can use Snell's law, which relates the angle of incidence to the angle of refraction:

$n = \frac{sin \theta_i}{sin \theta_r}$

where

$\theta_i$ is the angle of incidence

$\theta_r$ is the angle of refraction

Here we know

$\theta_i = 30^{\circ}$

So, we can find the angle of incidence:

$\theta_i = sin^{-1}(n sin \theta_r)=sin^{-1}((1.41)(sin 30))=44.8^{\circ}$

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