Question

A.) Sunlight strikes a piece of crown glass at an angle of incidence of 31.5deg. Calculate the difference in the angle of refraction between a yellow (580 nm) and a violet (410 nm) ray within the glass. The index of refraction is n=1.523 for yellow and n=1.538 for violet light. You have to calculate the angle of refraction for both light rays (they have different indices of refraction). You are looking for the difference of these angles.

B.) The ray now travels inside the glass. What is the minimum angle of incidence at which the yellow ray can hit the surface of the glass and become there totally internally reflected and not refracted? The angle of incidence is the angle with respect to the normal. Now the beam comes from inside and wants to leave the medium. Since the index of refraction of the medium is larger than 1 (index of refraction of air) there is a critical angle at which the beam is totally internally reflected.

Answer 1

A) The difference between angles of refraction of yellow and violet light can be determined as follows:

First find the refraction angle of each ray and then find the difference.

Apply Snell's law to calcualte the refractive angle of yellow light.

       

Here, i is the incident angle and r is the refractive angle.

Thus, the refractive angle for yellow light is,

     

       

          

Similarly, the refractive angle of the violet light is,

           

Thus, the difference between two refractive angles is,

       

Therefore, the difference in the refractive angles is .

B) The minimum angle of incidence can be determined as follows:

When the light travels from denser to rarer and the refractive angle becomes 90, then the angle of incidence is called criticall incidence.

Apply the Snell's law to find the incident angle.

Since the refracted angle becomes 90, thus

   

   

Rearrange the equation for incident angle:

  

Therefore, the crictical angle is .