Question

A ray of light is incident in air on a block of a transparent solid whose index of refraction is n. If , what is the largestangle of incidence for which total internal reflection will occur at the vertical face (point A shown in Fig. P33.39)?

Short answer

the largest angle will be 71.8 ° to have the total internal reflection

Step-by-step solution

About Total internal reflection

total internal reflection, in physics, complete reflection of a ray of light within a medium such as water or glass from the surrounding surfaces back into the medium. The phenomenon occurs if the angle of incidence is greater than a certain limiting angle, called the critical angle.

Determine the largest angle of incidence

To have the total internal reflection at point a in the vertical face refraction angle with the normal should be 90°- We will get

an critical angle at point A inside the glass for which Total internal reflection will happen. So from the Snell's Law We have:

Now in triangle ABC sum of the angles is 180°- 50,

Step A

Apply the Snell's Law again to get 00:

Hence, the largest angle will be 71.8 ° to have the total internal reflection-