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

  • Context: Undergrad 
  • Thread starter Thread starter rjs523
  • Start date Start date
  • Tags Tags
    Approximation Law
Click For Summary

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
Messages
4
Reaction score
0
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\theta1=n2\theta2

Thanks
 
Science news on Phys.org
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:
 

Similar threads

Graduate Interpretation of a complex angle of refraction
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is Snell's law incompatible with interface conditions? What went wrong?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate How to compute phase gradient from Snell's law?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Infinitesimal, Snell's law, and ray tracing
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Understanding a Generalization of Snell's Law
  • · Replies 19 ·
Replies
19
Views
6K
Plane wave angle of incidence calculation
  • · Replies 6 ·
Replies
6
Views
3K
High School Is there a shortcut for finding theta4 using Snell's Law when theta2 is known?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Snell's Law: Definition, Equations, Refractive Index & Critical Angle
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Is Snell's Law valid even when incident ray is Normal to the surface?
  • · Replies 3 ·
Replies
3
Views
3K
Apparent depth of an object underwater
  • · Replies 3 ·
Replies
3
Views
2K