Refraction and Total Internal Reflection

In summary: If you draw the ray going from air to glass, and then draw a perpendicular to the ray, the angle it makes with the normal will be 16.9 degrees.
  • #1
http://img210.imageshack.us/img210/6094/questionuz8.png [Broken]

i) What is the angle of refraction of the ray RS after it strikes the glass prism of refractive index=1.5?

ii) If the critical angle is 41.8 degrees, deduce whether the ray will suffer total internal reflection.


2. Homework Equations :

Snell's Law

3.

1) Snell's Law:

n=sin i / sin r

1.5=sin45/sinR

sinR * 1.5 = sin45
sinR = sin45 / 1.5
R = sin^-1 (sin45 / 1.5)
R= 28.1 degrees

2) I have no idea what I could do to deduce whether it would suffer TIR or not... please help. Thank you :)
 
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  • #2
total internal reflection occurs for angles greater than the critical angle, that should solve that one for you =].
 
  • #3
But you see the angle 28.1 isn't the incident angle made by the ray when its leaving the slow medium for the fast medium (glass => air).

I have to somehow find this incident angle, or so I assume >_> I hope to god it's not trigonometry, but I have a feeling it is as such V_V
 
  • #4
it will invole trig =P

draw the ray on the diagram, remembering the angle is with respect to the normal of the surface, then just have to work out the angle that it is going to cross the glass-air interface at

id draw a diagram of what i have, but this computer has nothing i can do that on -.-

basically, draw your rays, draw the normals to the two surfaces, and use trig to solve, it isn't THAT difficult.
 
  • #5
Ok... so it makes 28.1 degress... I think that the 90 degrees will be cut in half by the normal making a 45 degree angle in the triangle formed.

The problem now is that I can't identify where the angle is going to be formed with the normal...
 

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  • #6
http://www.omgimages.net/img/294/medium_54676.PNG [Broken]

since i haven't posted enough to put urls on yet =P

you want to calculate the angle between the ray and the normal, the red and grey lines on that diagram.
 
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  • #7
The angle will be 16.9 degress... so therefore no TIR occurs >_>

Thanks. This was an exam question. I therefor got it wrong ;_; I drew the normal in the wrong place.
 

What is refraction?

Refraction is the bending of light when it passes through a medium with a different optical density. This change in direction is due to the change in speed of light as it travels from one medium to another.

What is the law of refraction?

The law of refraction, also known as Snell's law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.

What is total internal reflection?

Total internal reflection is a phenomenon that occurs when a ray of light traveling from a denser medium to a less dense medium is reflected back into the denser medium instead of passing through. This happens when the angle of incidence is greater than the critical angle, which is the angle at which the refracted ray would be at a 90 degree angle to the normal.

What factors affect the amount of refraction?

The amount of refraction depends on the difference in optical density between the two media, the angle of incidence, and the wavelength of light. The greater the difference in density, the larger the angle of refraction will be. Additionally, shorter wavelengths of light are more strongly refracted than longer wavelengths.

What are some real-life examples of refraction and total internal reflection?

Refraction is responsible for the bending of light in lenses, such as in glasses or contact lenses. It also plays a role in the formation of rainbows and the mirage effect on hot surfaces. Total internal reflection is used in fiber optics for telecommunications and in the design of prisms and optical instruments.

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