Question

A light ray incident from medium 1 to medium 2, where n1>n2. When the incident angle exceed the critical angle ac, the refracted angle exceed 90o, which means no light transmitted into medium 2. This is known as the total internal reflection. What is the critical angle "ac" (ac<90 degree) for total internal reflection to occur

Answer 1

Answer:

The critical angle is  $ac =sin^{-1}\frac{n_2}{n_1}$

Explanation:

  Snell's law is mathematically represented as

                    $n_1 sin \theta_1 = n_2 sin \theta_2$

Where $n_1$ is the refractive index of medium 1

           $n_2$ is the refractive index of medium 2

Now substituting $90^o$ for $\theta_2$ and ac which denotes the critical angle for $\theta_1$

             $n_1 sin (ac) = n_2 \ sin(90)$

Making ac the subject

                 $ac =sin^{-1}\frac{n_2}{n_1}$

From the question we are told that $n_1 > n_2$

 The is implies that ac < 90

            since  $\frac{n_2}{n_1} < 1$

Critical angle is that angle of incidence that result to a 90 degree angle of refraction