Refraction and total internal reflection

[calgal260]

A mixture of red and violet light is incident on a glass-air interface. The indices of refraction for red and violet light in glass are n(red)=1.52 and n(violet)=1.538. What color of light enters the air?

http://www.webassign.net/cj8/q_10.gif

attempt to solve:
I found that the critical angle for the violet light is 40.56 degrees and 41.14 degrees for the red. If the critical angle for the red light is larger, shouldn't there be total internal reflection?

Thanks in advance!

 

[ehild]

At which angle does total reflection happen? Greater or lower than the critical angle?

ehild

 

[calgal260]

At which angle does total reflection happen? Greater or lower than the critical angle?

ehild

Greater than the critical angle, right? That is what I'm getting but this problem is confusing. I must be doing something wrong.

 

[ehild]

The light enters at the glass-air interface at 40.85° angle. For which light is this angle greater than the critical one?

ehild

 

[rwisz]

I would like to clarify that refraction is the bending of light as it passes through different mediums, while total internal reflection occurs when a light ray is completely reflected within a medium due to the angle of incidence being greater than the critical angle.

In this scenario, the mixture of red and violet light is incident on a glass-air interface, where the indices of refraction for red and violet light in glass are n(red)=1.52 and n(violet)=1.538. This means that the speed of light is slower in glass than in air, causing the light to bend as it enters the glass. The amount of bending depends on the wavelength of the light, with shorter wavelengths (such as violet light) bending more than longer wavelengths (such as red light).

Based on the given indices of refraction, we can calculate the critical angle for each wavelength using the formula sinθc = n2/n1, where n2 is the index of refraction for air (which is approximately 1) and n1 is the index of refraction for glass. For red light, the critical angle is 41.14 degrees, and for violet light, it is 40.56 degrees. This means that for the violet light, the angle of incidence would need to be larger than 40.56 degrees in order for total internal reflection to occur, while for red light, the angle of incidence would need to be larger than 41.14 degrees.

To answer your question, the color of light that enters the air in this scenario would be a mixture of red and violet light, with the violet light being slightly more bent than the red light due to its shorter wavelength. The amount of bending for each color can be calculated using the formula θ = sin^-1(n2/n1), where θ is the angle of refraction. So for violet light, the angle of refraction would be approximately 25.37 degrees, while for red light, it would be approximately 24.78 degrees.

In conclusion, the critical angle for a specific wavelength of light depends on the index of refraction of the medium it is passing through. While the critical angle for violet light is smaller than that of red light in this scenario, it does not necessarily mean that total internal reflection will occur for violet light. The specific angle of incidence and the angle of refraction also play a role in determining whether total internal reflection will occur.