# Fresnel Double Prism equation

1. Jan 23, 2005

### jh

Hi,
i need to deduce the Fresnel Double Prism equation, which states:

d = 2a(n-1)alpha,

Fresnel Double Prism setup

The distance between the constructed virtual objects S' and S'' is here called d. The distance from the light source to the prism is called a, the prism has two sides (common base) defined by the common apex angle alpha, and the refractive index n.

Any help appreciated!!

2. Jan 23, 2005

### clive

Hi jh,

You probably know that for a single prism the deviation angle is given by
$$\delta=i+i'-A$$
The refraction' law in the incidence and emergence points (for very small angles) is
$$i=nr$$
$$nr'=i$$
and from these two equations you have now
$$i+i'=n(r+r')=nA$$.

It is clear now that
$$\delta=nA-A=A(n-1)$$

Because you have a double prism,
$$\delta_{tot}=2\delta$$.
and $$\delta_{tot}\cdot a$$ for the distance between the two points (images). ( $$A=\alpha$$)

Last edited: Jan 23, 2005