Interference of light Intensity

• mbnMecha
In summary: So you should use the diffraction formula to find the intensity at theta1 and theta2, and then multiply the result with the interference factor.
mbnMecha
An Interference pattern is produced by light of wavelength 490nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of d=0.630mm.
a) If the slits were very narrow what would be the angular position theta1 and theta2 of the first and second lateral interference maxima?
b)Let the slits have width a=0.42 mm. In terms of the intensity I0 at the center of the central maximum, what is the intensity at each of the angular positions theta1 and theta2

Homework Equations

Intensity of light during diffraction:
I=Im (sinx/x)^2 where I am is the max intensity and x=phase difference/2 = (pi*a*sin(theta))/wavelength
Intensity of light during interference
I=4I0cos^2(z) where z = phasedifference/2 = (pi*d*sin(theta))/wavelength

Intensity of light during double slit diffraction
I=Imcos^2(z)*(sinx/x)^2)

The Attempt at a Solution

I have solved for theta1 and theta2 and got:
theta1=7.78 x 10^(-4) rd
theta2= 1.55 x 10^(-3) rdWhat I can't seem to understand is how to find part the intensities in part b. the question does not mention whether we should take the Effects of diffraction into consideration and I don't know what formula to use. what should I do?

mbnMecha said:
What I can't seem to understand is how to find part the intensities in part b. the question does not mention whether we should take the Effects of diffraction into consideration
You have to take them into account, otherwise there won't be an intensity change. This diffraction is an interference effect as well, by the way.
mbnMecha said:
and I don't know what formula to use.
The one you have posted.

mfb said:
You have to take them into account, otherwise there won't be an intensity change. This diffraction is an interference effect as well, by the way.The one you have posted.
I have posted 3 equations.. does that mean I have to consider the equation with both the interference and the diffraction factors? thanks in advance.

Well, you know the result of the "interference formula" already: you are calculating the intensity of a maximum.

1. How does interference of light intensity occur?

Interference of light intensity occurs when two or more light waves overlap and interact with each other. This can result in either constructive interference, where the waves amplify each other, or destructive interference, where the waves cancel each other out.

2. What factors affect the interference of light intensity?

The interference of light intensity can be affected by several factors, including the distance between the light sources, the wavelength of the light, and the angle at which the waves intersect.

3. What is the difference between interference of light intensity and interference of sound waves?

The main difference is that light waves are transverse waves, meaning they oscillate perpendicular to the direction of propagation, while sound waves are longitudinal waves, meaning they oscillate parallel to the direction of propagation. Additionally, light waves can interfere with each other even at large distances, while sound waves require a medium to propagate.

4. How is interference of light intensity used in real-world applications?

Interference of light intensity is used in many practical applications, such as in optical coatings for reducing glare, in thin film interference for creating colorful patterns, and in interferometry for measuring small changes in distance or detecting small vibrations.

5. Can interference of light intensity be observed in everyday life?

Yes, interference of light intensity can be observed in everyday life. For example, when you see a rainbow or the colorful patterns on a soap bubble, you are witnessing the interference of light waves. It can also be seen in the iridescent colors of certain insects and the shimmering patterns on a CD or DVD.

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