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

[rjs523]

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$$\theta$$1=n2$$\theta$$2

Thanks

 

[Doc Al]

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!

 

[tiny-tim]

welcome to pf!

hi rjs523! welcome to pf!

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

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 … ? ​

 

[rjs523]

Thanks a lot for the help and the warm welcome