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

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Simplifying Snell's Law to n1θ1=n2θ2 is a valid approximation for angles below 10 degrees, as the sine function can be approximated by the angle in radians. This simplification provides sufficient accuracy for practical applications within that range. It is important to measure angles in radians to ensure the approximation holds true. The discussion also notes that errors in the sine terms tend to cancel each other out, further supporting the validity of the approximation. Overall, this method can be effectively used for small angle scenarios in optics.
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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\theta1=n2\theta2

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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