Intensity of Double Slit Pattern

[lha08]

Homework Statement

Could anyone help me to explain how the intensity of the double Slit pattern works because I'm looking at the formula and I'm really confused...

Homework Equations

I=4Icos^2(phi/2)
A=2Ecos(phi/2)

The Attempt at a Solution

 

[dx]

What specifically do you want explained? The formula is easy to derive geometrically using the phasor diagram. Or you can do it algebraically: since only the phase difference matters, let the complex amplitude from slit one be just A (a real number). Then the complex amplitude from slit two will be Ae^iφ. The sum is therefore A(1 + e^iφ) = A(1 + cosφ + isinφ), and the magnitude squared is A²(1 + cos²φ + 2cosφ + sin²φ) = A²(2 + 2cosφ) = 2A²(2cos²(φ/2)) = 4A²cos²(φ/2).

 

[nlightner]

The intensity of the double slit pattern is determined by the interference of two coherent light waves passing through two slits. This interference results in a pattern of bright and dark fringes on a screen behind the slits. The intensity of the pattern is strongest at the center of the pattern, where the two waves are in phase and constructively interfere, and decreases as you move away from the center.

The formula you mentioned, I=4Icos^2(phi/2), is known as the intensity equation and it describes the relationship between the intensity of the pattern (I) and the phase difference between the two waves (phi). This equation shows that the intensity of the pattern is directly proportional to the square of the cosine of half the phase difference.

The second equation, A=2Ecos(phi/2), relates the amplitude of the pattern (A) to the electric field amplitude (E) and the phase difference (phi). This equation shows that as the phase difference increases, the amplitude of the pattern decreases.

In summary, the intensity of the double slit pattern is determined by the interference of two coherent waves, and is strongest at the center of the pattern where the waves are in phase. The intensity equation and the amplitude equation can be used to quantitatively describe the behavior of the pattern.