Question

A beam 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.

Answer 1

Answers:

1) 1.359, 1.403

2) $2.207(10)^{8}m/s$,  $2.138(10)^{8}m/s$    

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 $n$ 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 ($c=3(10)^{8}m/s$) and the speed of light $v$ in the second medium:

$n=\frac{c}{v}$   (1)

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

$n_{1}sin(\theta_{1})=n_{2}sin(\theta_{2})$   (2)  

Where:  

$n_{1}$ is the first medium refractive index . We are told is the air, hence $n_{1}\approx 1$

$n_{2}$ is the second medium refractive index  

$\theta_{1}$ is the angle of the incident ray  

$\theta_{2}$ is the angle of the refracted ray  

Knowing this, let's begin with the answers:

1) Indexes of refraction for red and violet light

1a) Red light

Using equation (2) according to Snell's Law and $\theta_{1}=57.0\º$   $\theta_{2}=38.1\º$:

$(1)sin(57.0\º)=n_{2}sin(38.1\º)$  

Finding $n_{2}$:

$n_{2}=\frac{sin(57.0\º)}{sin(38.1\º)}$  

$n_{2}=1.359$   (3)>>>Index of Refraction for red light

1b) Violet light

Again, using equation (2) according to Snell's Law and $\theta_{1}=57.0\º$   $\theta_{2}=36.7\º$:

$(1)sin(57.0\º)=n_{2}sin(36.7\º)$  

Finding $n_{2}$:

$n_{2}=\frac{sin(57.0\º)}{sin(36.7\º)}$  

$n_{2}=1.403$   (4) >>>Index of Refraction for violet light

2) Speeds of red and violet light

1a) Red light

Here we are going to use equation (1):

$n_{red}=\frac{c}{v_{red}}$

$v_{red}=\frac{c}{n_{red}}$

Substituting (3) in this equation:

$v_{red}=\frac{3(10)^{8}m/s}{1.359}$

$v_{red}=2.207(10)^{8}m/s$ >>>>Speed of red light

1a) Violet light

Using again equation (1):

$n_{violet}=\frac{c}{v_{violet}}$

$v_{violet}=\frac{c}{n_{violet}}$

Substituting (4) in this equation:

$v_{violet}=\frac{3(10)^{8}m/s}{1.403}$

$v_{red}=2.138(10)^{8}m/s$ >>>>Speed of violet light