# Help Deriving Fresnel's Equations Please

• Fjolvar
In summary, the conversation discusses the process of deriving/simplifying Fresnel's equation for r perp. The speaker mentions using Snell's law and a trigonometric identity to make substitutions, but is having trouble getting rid of the square root in order to obtain the desired trigonometric form. They ask for help or a hint with the derivation.
Fjolvar
I'm trying to derive/simplify Fresnel's equation for r perp from its form:

[ni cos $$\theta$$i - nt cos$$\theta$$ t] / [ni cos $$\theta$$ i + ntcos$$\theta$$t]

to ---> - sin ($$\theta$$i - $$\theta$$t) / sin ($$\theta$$i + $$\theta$$t)

From what I've gathered you need to use Snell's law ntsin$$\theta$$t = nisin$$\theta$$i

and also substitute the identity cos^2$$\theta$$ = $$\sqrt{1-sin^2\theta}$$

I've been playing with the substitutions along with the trig identity Sin (a-b) = sinacosb - cosasinb... but i cannot get it to work. Any help would be greatly appreciated. I'm stuck mostly on getting rid of the square root after making the substitution to get the trig identity form. Thanks.

Last edited:
Even a hint will be appreciated if you don't want to show the derivation.

## 1. What are Fresnel's equations?

Fresnel's equations are a set of mathematical equations that describe the behavior of light when it passes through an interface between two different materials.

## 2. Why do we need to derive Fresnel's equations?

Deriving Fresnel's equations allows us to understand the fundamental principles of how light behaves at interfaces, and it also allows us to make predictions about the behavior of light in different materials and under different conditions.

## 3. How do we derive Fresnel's equations?

Fresnel's equations can be derived using Maxwell's equations, which describe the behavior of electromagnetic waves. The equations involve solving for the electric and magnetic fields at the interface between two materials.

## 4. What is the significance of Fresnel's equations?

Fresnel's equations are important in a wide range of applications, including optics, electronics, and materials science. They help us understand and predict the behavior of light in various materials and are essential for the development of many technologies.

## 5. Are Fresnel's equations derived differently for different materials?

Yes, the derivation of Fresnel's equations may vary slightly depending on the specific properties of the materials involved. For example, the equations may be different for materials with different refractive indices or for materials with different polarizations.

• Introductory Physics Homework Help
Replies
5
Views
2K
Replies
18
Views
3K
• Calculus
Replies
4
Views
2K
• Calculus
Replies
4
Views
885
Replies
4
Views
3K
Replies
11
Views
2K
Replies
2
Views
1K
• Precalculus Mathematics Homework Help
Replies
9
Views
2K
• Precalculus Mathematics Homework Help
Replies
21
Views
3K