Physical Optics

Prerequisite: algebra2, physics

This is the diffraction equation from regular physics:

dsinθ = mλ (m = 0, 1, 2, 3..)

in which d is the distance between two slits

and m is the order at which there is a maximum.

Here is a twin equation:

Dsinθ = mλ (m = 1, 2, 3, 4..)

in which D is the distance of a slit's width

and m is the order at which there is a minimum.

This twin equation can be shifted by half a wavelength to describe maximums:

Dsinθ = (m - 1/2)λ (m = 1, 2, 3, 4..)

in which D is the distance of a slit's width

and m is the order at which there is a maximum.

And the regular can be shifted to describe minimums. So there. The basis of the equation is this:

dsinθ = mλ

path difference = phase difference

This equation can be adapted for soap bubbles and the like, applicable only for perpendicular light rays (note that the diagram slants the rays for demonstration purposes):

path difference = phase difference

2t = (λ / n)

Where t is the medium's thickness

and n is the index of refraction through a medium.

And really, you can use any combination you like~

dsinθ = mλ = 2t = (λ / n)

Here are some laws on polarization. Malus' law tells the output intensity of a light ray going through polaroids at a certain angle, which is essentially the component aligned with the transmission axis. Brewster's law tells the incidence angle at which light is polarized. Interestingly, the sum of the angle of polarization and angle or refraction is 90˚ (θp + θr = 90˚).

If you find polarization fascinating, you ought to know about Quantum Cryptography~ In fact, everyone ought to know about it!