Is Simplifying Snell's Law to n1θ1=n2θ2 Valid for Small Angles?

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Discussion Overview

The discussion revolves around the validity of simplifying Snell's Law to the form n1θ1=n2θ2 for small angles, specifically angles below 10 degrees. Participants explore the implications of this approximation in the context of physics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions whether the sine terms can be omitted from Snell's Law for small angles, suggesting that the approximation n1θ1=n2θ2 might be valid.
  • Another participant agrees that this simplification could be a good approximation within the specified range of angles and suggests checking examples for accuracy, emphasizing the importance of measuring angles in radians.
  • A third participant provides a mathematical insight regarding the errors involved in the approximation, noting that the errors in the sine terms would partially cancel each other out.

Areas of Agreement / Disagreement

Participants generally agree that the approximation may hold for small angles, but there is no consensus on the extent of its validity or the specific conditions under which it applies.

Contextual Notes

Limitations include the dependence on the range of angles considered and the potential errors introduced by the approximation, which have not been quantitatively resolved in the discussion.

Who May Find This Useful

This discussion may be useful for students and educators in physics, particularly those interested in optics and the application of Snell's Law in practical scenarios involving small angles.

rjs523
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Can you take the sin terms out of Snell's Law when dealing with angles below 10 degrees? so Snell's Law would be become n1[tex]\theta[/tex]1=n2[tex]\theta[/tex]2

Thanks
 
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That would be a fairly good approximation as long as the angles stay within that range. (Do a few examples to check that it gives you sufficient accuracy for your needs.) Be sure to measure the angles in radians!
 
welcome to pf!

hi rjs523! welcome to pf! :smile:

(have a theta: θ and a degree: ° and try using the X2 icon just above the Reply box :wink:)

the error in one sine would be (θ3/6)/θ, or θ2/6

since both errors would be in the same direction, they will to some extent cancel out,

to … ? :smile:​
 
Thanks a lot for the help and the warm welcome :smile:
 

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