Understanding Light Dispersion in Equilateral Prisms for Beginners

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In summary, Dani has determined that the angle of refraction is 28.135 degrees and that Snell's law fails her in determining the angle of reflection.
  • #1
iamnotbatman
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I feel rather stupid for not understanding this, but it's really thrown me for a loop, so any help would be greatly appreciated!

A ray of light is incident at 45 degrees on an equilateral glass prism (n=1.5).

So far, I have determined the angle of refraction to be 28.135 degrees, using Snell's Law of course, and the measures of several arbitrary internal angles using basic geometry, including what I believe to be the second angle of incidence, at 31.865 degrees. What has me stumped is the angle of refraction back out of the prism. Snell's Law fails me here, and I do believe it is because I'm overlooking something about the dispersion of the light into its component colors... but I have no idea what to do, because other than the fact that red bends the least and violet bends the most, I don't understand dispersion... a nudge in the right direction would be awesome, please

Thank you!
-Dani
 
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  • #2
iamnotbatman said:
What has me stumped is the angle of reflection back out of the prism. Snell's Law fails me here, and I do believe it is because I'm overlooking something about the dispersion of the light into its component colors...

First of all, I'm going to assume that you mean refraction, not reflection (the angle of reflection is the same as the angle of incidence). If you assume all the light is refracted at the same angle (that is, constant n), then chromatic dispersion is being neglected. Using Snell's law:

[tex]sin(\theta_i)=nsin(\theta_r)[/tex]

where the angle on the left is the incident and angle and the one on the right is the refracted angle, while n is the index of refraction in water. You say this formula fails you for the outgoing ray, but consider that there is symmetry here. That is, the path that a light ray travels from one medium to another is the same path as would be followed going in the other direction. This means that you can reverse the problem and imagine a light ray hitting the prism with an unknown angle and then bending to an angle of 31.865 degrees (assuming you did the geometry right). Solving from the above equation, this means:

[tex]sin(\theta_r)=\frac{sin(\theta_i)}{n}[/tex]

This should give you the same angle as for a light ray coming from the prism at 31.865 degrees and bending in the air.
 
  • #3
Yes, I did mean refraction. Thanks for pointing out the horrid typo lol. *slaps self on wrist*

Thank you very much for your help!
 

Related to Understanding Light Dispersion in Equilateral Prisms for Beginners

1. What is dispersion?

Dispersion is the phenomenon where white light is split into its component colors as it passes through a medium, such as a prism or water droplets. This is due to the different wavelengths of light traveling at different speeds through the medium.

2. How do prisms work?

Prisms work by refracting (bending) light at different angles based on its wavelength. This causes the light to separate into its component colors, creating a rainbow effect. Prisms are often used in optics to manipulate and disperse light.

3. What is the difference between dispersion and refraction?

Dispersion and refraction are both optical phenomena that involve the bending of light. However, dispersion specifically refers to the separation of light into its component colors, while refraction is the bending of light as it passes through a medium with a different density.

4. Can dispersion be used for anything besides creating rainbows?

Yes, dispersion has many practical applications in various fields. For example, it is used in spectroscopy to analyze the composition of substances, in telecommunications to separate and transmit different wavelengths of light, and in photography to create special effects.

5. What other factors can affect dispersion besides the medium?

The angle at which the light enters the medium can also affect dispersion. The higher the angle, the more the light will be dispersed. Additionally, the temperature and pressure of the medium can also impact the speed of light and therefore affect the amount of dispersion that occurs.

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