Getting Brewster's Formula from Snell's Law

In summary, using Snell's Law equation 2 and the fact that θ1 + θ2 = 90°, we can derive the Brewster's angle formula given by equation 4, where tanθB = n2/n1. This is done by substituting θ2 = 90 - θ1 and applying the definition of sine and cosine in a right triangle.
  • #1
coldjeanz
22
0
From Snell’s Law equation (2) get the Brewster’s angle formula given by equation (4) when θincident+θrefracted=90°.

equation 2: n1 sin θ1 = n2 sinθ2

equation 4: tanθB = n2/n1

This is kind of foreign to me as I haven't studied it yet, not sure how you go from Eq 2 to E4, how does tan come from an equation with 2 sin in it?
 
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  • #2
You know that θ1 + θ2 = 90. Try subing in θ2 = 90 - θ1.
 
  • #3
so then I would eventually end up with:

sinθ1/sin(90-θ1) = n2/n1

still not sure how the left side turns into tanθb though...
 
  • #4
Remember the definition of sine and cosine of the angles in a right triangle.

ehild
 
  • #5
Since you know the answer, you can take a peek at it and then look back at what you currently have. What must sin(90-θ1) to transform where you are into the answer? The next question is "does sin(90-θ1) equal what it needs to equal?"
 

FAQ: Getting Brewster's Formula from Snell's Law

1. What is Brewster's Formula?

Brewster's Formula is an equation that relates the angle of incidence and the refractive index of a material, allowing us to calculate the angle of reflection for light passing through that material. It is named after Sir David Brewster, a Scottish physicist and inventor.

2. How is Brewster's Formula derived from Snell's Law?

Brewster's Formula is derived from Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials. By manipulating this equation and using trigonometric identities, we can arrive at Brewster's Formula.

3. What is the significance of Brewster's Angle?

Brewster's Angle is the angle of incidence at which light is polarized when it reflects off a surface. This means that all light waves are vibrating in the same plane, making it useful in applications where polarized light is needed, such as in polarized sunglasses.

4. What are the units of measurement for Brewster's Formula?

The units of measurement for Brewster's Formula are in degrees or radians, depending on the unit used for the angle of incidence and angle of refraction. The refractive index is a unitless value, so no units are needed for that part of the equation.

5. Can Brewster's Formula be applied to all materials?

No, Brewster's Formula can only be applied to transparent materials with refractive indices greater than 1. This is because the formula relies on the concept of refraction, which only occurs when light passes through a material with a different refractive index. Additionally, it is only valid for unpolarized light.

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