# Refractive index

1. May 19, 2011

### mogley76

1. The problem statement, all variables and given/known data

a ray of light travelling through glass is incident at the interface with air at an angle of 30 deg to the normal. if the ray is refracted at the critical angle, what is the refractive index of the glass?

2. Relevant equations

none

3. The attempt at a solution

sin (90)= n2/n1 therefore n = 1 is that right?

2. May 19, 2011

### frozenguy

n of the glass can't equal 1, because that is for vacuum. And air is like n=1.0003 or something .

If the light incident on a barrier is incident at an angle less than the critical angle, light will refract through. If its more than the critical angle, the light will internally reflect.

This holds for light incident on an interface traveling in a material with a greater index of refraction than the material the light wants to enter.

So for this to even be possible, you know n of glass is going to be bigger than 1.0003.

Do you know snells law? You need that equation and the equation for the critical angle.
Do you have a reference to find those and read what comes with it?

Last edited: May 19, 2011
3. May 19, 2011

### mogley76

sin crit angle =n2 right?

4. May 19, 2011

### frozenguy

Not quite.

$$sin\left(\theta_{c}\right)=\frac{n_{2}}{n_{1}}$$

So $$\theta_{c} = sin^{-1}\left(\frac{n_{2}}{n_{1}}\right)$$
n1 is the medium the light is in, n2 is the index of air which is 1.0003

5. May 19, 2011

### rl.bhat

You can use a general expression
n1sin(θ1) = n2sin(θ2)
suffix 1for the incident medium and 2 for the refracted medium.
When the angle of incidence in the denser medium is equal to the critical angle, the angle of refraction in the rarer medium is 90o.

6. May 20, 2011

### SammyS

Staff Emeritus
This should be: sin(30°)/sin(90°)= n2/n1 , where n2 is the refractive index of air.