Light enters a transparent material from air at 30.0° to the normal. It continues within the material at the angle of refraction of 23.0°. What is the critical angle for total internal reflection when this material is surrounded by air?

The value is

Explanation:

From the question we are told that

    The angle of incidence is  

    The angle of refraction is  

Generally at the point where the light enters the material ,  from Snell's law  we have that

Here  n is the refractive index of the material

=>        

=>        

Generally for total internal  reflection , the critical angel is evaluated using Snell law as follows

=>        

=>      

=>    

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