# Fresnel equation and Snell's law

## Homework Statement

Use Snell's law to show fresnel Eq 1 can be expressed as Eq 2

Eq 1 = (ncosθ-n'cosθ') / (ncosθ+n'cosθ)
Eq 2 = (tanθ' - tanθ) / (tanθ' + tanθ)

## Homework Equations

nsinθ=n'sinθ' (Snell's law)

## The Attempt at a Solution

n' = nsinθ / sinθ'

Substitute n' into equation and then multiply numerator and denominator by sinθ'/n gives:

(cosθsinθ'-cosθ'sinθ) / (cosθsinθ'+cosθ'sinθ)

I'm not sure how to get from here to Eq 2 though. I know sinθ/cosθ = tanθ and cosθ/sinθ=1/tanθ.

TSny
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Gold Member
(cosθsinθ'-cosθ'sinθ) / (cosθsinθ'+cosθ'sinθ)
Divide numerator and denominator by an appropriate expression.

cosθ?

TSny
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Gold Member
Consider the first term in your numerator: cosθ⋅sinθ'

What would you have to divide this by to get the first term in the numerator of Eq 2?

cosθ'/cosθ

TSny
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Gold Member
cosθ'/cosθ
Not quite.

cosθ⋅sinθ'*1/cosθ'*cosθ=tanθ'

TSny
Homework Helper
Gold Member
cosθ⋅sinθ'*1/cosθ'*cosθ=tanθ'
OK. So you divided by cosθ'*cosθ (not cosθ'/cosθ).

Good. This suggests seeing what happens if you divide the top and bottom of (cosθsinθ'-cosθ'sinθ) / (cosθsinθ'+cosθ'sinθ) by cosθ'*cosθ.