Abeam of light strikes a sheet of glass at an angle of 57.0° with the normal in air. you observe that red light makes an angle of 38.1 degrees with the normal in the glass, while violet light makes a 36.7 degree angle.
1.what are the indexes of refraction of this glass for these colors of light?
answer in the order indicated. separate your answers with a comma.

2.what are the speeds of red and violet light in the glass?
answer in the order indicated. separate your answers with a comma.

1) 1.359, 1.403

2) ,      

Explanation:

The described situation is known as Refraction.  

Refraction is a phenomenon in which a wave (the light in this case) bends or changes it direction when passing through a medium with a refractive index different from the other medium.  

In this context, the Refractive index is a number that describes how fast light propagates through a medium or material, and is defined as the relation between the speed of light in vacuum () and the speed of light in the second medium:

  (1)

On the other hand we have the Snell’s Law:  

  (2)  

Where:  

is the first medium refractive index . We are told is the air, hence

is the second medium refractive index  

is the angle of the incident ray  

is the angle of the refracted ray  

Knowing this, let's begin with the answers:

Using equation (2) according to Snell's Law and   :

Finding :

  (3)>>>Index of Refraction for red light

Again, using equation (2) according to Snell's Law and   :

Finding :

  (4) >>>Index of Refraction for violet light

Here we are going to use equation (1):

Substituting (3) in this equation:

>>>>Speed of red light

Using again equation (1):

Substituting (4) in this equation:

>>>>Speed of violet light