Young's double slit and interference maximums

[DWill]

Homework Statement

In a Young's double slit experiment the width of each slit is a, the distance between the centers
of the slits is d, and the 10th interference maximum to the right of the central maximum is the first
missing maximum. a) Find the ratio of the slit separation distance to the width, d
a
b) Find the number of interference maximums across the central diffraction maximum.
c) Find the ratio of the intensity of the 5th interference maximum relative to intensity of the
central maximum.

Homework Equations

phi = (2pi / lambda) * d * sin(theta)
beta = (2pi / lambda) * a * sin(theta)

The Attempt at a Solution

(a) I see that the ratio d/a is phi/beta, but how do I determine the value of phi and beta? All I can think of is that the 1st minimum occurs at beta = 2pi, but I'm not sure how that would relate here.
(b) No idea on this one
(c) There's a long equation for I that relates it to I_o. It also includes cos^2 (phi/2) and also sin(beta/2), and is too long and I'm not sure how to write it here. I can figure this out I think if I know the value of either phi or beta, and then use the d/a ratio from part (a) to find the other value. Once I have those 2 I can use the equation to relate the 5th interference maximum intensity to I_o (central max intensity).

Some explanations will also be greatly appreciated!

 

[Redbelly98]

Your textbook should have an equation for the intensity of a single-slit diffraction pattern. You will need that.

There should also be an equation for the interference maximums.

 

[thomate1]

I can provide some insight on the Young's double slit experiment and the concept of interference maximums. In this experiment, light from a single source is passed through two narrow slits, creating two coherent light sources. The light from these sources then interferes with each other, producing a pattern of light and dark fringes on a screen placed behind the slits.

(a) The value of phi and beta can be determined using the equations given in the problem, where lambda is the wavelength of the light and theta is the angle at which the interference pattern is observed. The value of phi can be calculated using the distance between the centers of the slits (d) and the angle (theta) at which the 10th interference maximum is observed. Similarly, the value of beta can be calculated using the width of each slit (a) and the same angle (theta). Once the values of phi and beta are known, the ratio d/a can be calculated.

(b) The number of interference maximums across the central diffraction maximum can be determined by using the equation m = (d/a) * (lambda/d), where m is the number of maximums. In this case, m = 10, so the number of maximums across the central maximum would be 10.

(c) The intensity of the 5th interference maximum can be calculated using the equation I = I_o * cos^2 (phi/2) * sin^2 (beta/2), where I_o is the intensity of the central maximum. The value of phi and beta can be calculated using the values obtained in part (a). Using this equation, the ratio of the intensity of the 5th interference maximum to the intensity of the central maximum can be determined.

I hope this helps in understanding the concepts of Young's double slit experiment and interference maximums.