(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A photomultiplier (PMT) is arranged to detect the photons from a double-slit experiment. It is placed at a point P in the detection plane and makes an angle [tex]\theta[/tex] with the horizontal of one of the slits. Assume that the two slits have different widths and that the widths are much less than the wavelength of light, [tex]\lambda[/tex].

The probability amplitude for a single photon of wavelength [tex]\lambda[/tex] to strike the PMT from one of the slits is [tex]\sqrt{2}[/tex] more than for the other slit. Calculate the visibility of the interference fringes:

[tex]V=\frac{P_{max} - P_{min}}{P_{max}+P_{min}}[/tex]

Where [tex] P_{max}[/tex] is the maximum probability and [tex]P_{min}[/tex] is the minimum probability that a photon is detected.

2. Relevant equations

[tex]A = A_1 + A_2[/tex] (amplitudes are summed)

[tex]P = (Abs(A_1 + A_2))^2[/tex] (probability is sum of amplitudes squared)

3. The attempt at a solution

I let [tex]A_1[/tex] be the greater amplitude, so it is equal to [tex]A_2 + \sqrt{2}[/tex]. Then I use the equation for probability above to solve for [tex]A_2[/tex].

First problem:

I get different results if I solve it by hand or if I use Mathematica. Solving by hand I find that [tex]A_2 = A_1 = \frac{1-\sqrt{2}}{2}[/tex], but Mathematica tells me that [tex]A_2 = -1.20711 < 0[/tex] or [tex]A_2 = -0.207107 < 0[/tex]

The answer Mathematica gives is in decimal format...but the fact that it comes up negative is really confusing me...I feel like the amplitude must be positive...?

Second problem:

If I take the answer I calculate by hand and add the amplitudes and square to find the probability I get:

[tex]P = A_1 + A_2 = (Abs(\frac{1-\sqrt{2}}{2} + \frac{1-\sqrt{2}}{2}))^2 = 3 - 2\sqrt{2} = 0.171573 < 1[/tex]

The probability should sum to one, but it is much less than one.

What am I doing wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculating visibility of interference fringe

**Physics Forums | Science Articles, Homework Help, Discussion**