Refractive Index at Critical Angle: Find the Solution

In summary, the refractive index of glass can be found using the equation sin(30°)/sin(90°)= n2/n1, where n2 is the refractive index of air.
  • #1
mogley76
19
0

Homework Statement



a ray of light traveling 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?


Homework Equations



none

The Attempt at a Solution



sin (90)= n2/n1 therefore n = 1 is that right?
 
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  • #2
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:
  • #3
sin crit angle =n2 right?
 
  • #4
mogley76 said:
sin crit angle =n2 right?

Not quite.

[tex]sin\left(\theta_{c}\right)=\frac{n_{2}}{n_{1}}[/tex]

So [tex]\theta_{c} = sin^{-1}\left(\frac{n_{2}}{n_{1}}\right)[/tex]
n1 is the medium the light is in, n2 is the index of air which is 1.0003
 
  • #5
mogley76 said:
sin crit angle =n2 right?

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
mogley76 said:

The Attempt at a Solution



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

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

1. What is the refractive index at the critical angle?

The refractive index at the critical angle is the ratio of the speed of light in a vacuum to the speed of light in a medium at the critical angle.

2. How is the refractive index at the critical angle calculated?

The refractive index at the critical angle is calculated by taking the inverse sine of the ratio of the speed of light in a vacuum to the speed of light in the medium at the critical angle.

3. What is the significance of the refractive index at the critical angle?

The refractive index at the critical angle is significant because it determines the maximum angle at which light can travel through a medium without being refracted. This is known as total internal reflection and is used in many optical devices.

4. How does the refractive index at the critical angle vary with different materials?

The refractive index at the critical angle varies with different materials because it depends on the optical properties of the material, such as its density and composition. Materials with higher refractive indices will have a lower critical angle, while those with lower refractive indices will have a higher critical angle.

5. Can the refractive index at the critical angle be greater than 1?

Yes, the refractive index at the critical angle can be greater than 1. This is because the critical angle is determined by the ratio of the speed of light in a vacuum to the speed of light in the medium, and some materials have a higher speed of light in a vacuum than others, resulting in a refractive index greater than 1.

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