How Do You Calculate Path-Length Differences in Two-Source Interference?

[aliaze1]

Homework Statement

http://session.masteringphysics.com/problemAsset/1014010/14/1014010E.jpg

What are the path-length differences at Points A, C, and D
(respectively, ΔdA, ΔdC, ΔdD)?

Enter your answers numerically in terms of lambda λ

Homework Equations

Does this require an equation? I figured it was pictorial

http://session.masteringphysics.com/problemAsset/1014010/14/1014010D.jpg

The Attempt at a Solution

I looked at the picture and tried the following, which were all incorrect:

3.5, 2.5, 2
3, 2, 1.5

 

[aliaze1]

got it lol

nevermind, i got it, i used this:

http://session.masteringphysics.com/problemAsset/1014010/14/1014010F.jpg

 

[m2003]

2.5, 2, 1.5

First, let's define what we mean by "path-length difference." In the context of two-source interference, this refers to the difference in the distance traveled by light from two different sources to a specific point on a screen. This difference can affect the interference pattern observed at that point.

In the first image, we can see that there are two sources of light (represented by the red and blue lines) and a screen with three points labeled A, C, and D. The path-length differences at these points can be calculated by measuring the distance from each source to the point and taking the difference between the two.

At point A, the path-length difference would be the difference between the distance from source 1 to A and the distance from source 2 to A. In this case, it would be (1.5λ - 1λ) = 0.5λ.

At point C, the path-length difference would be the difference between the distance from source 1 to C and the distance from source 2 to C. In this case, it would be (2.5λ - 1.5λ) = 1λ.

At point D, the path-length difference would be the difference between the distance from source 1 to D and the distance from source 2 to D. In this case, it would be (2.5λ - 2λ) = 0.5λ.

In the second image, the path-length differences at points A, C, and D would be the same as the first image since the distances from the sources to the points are the same.

In summary, the path-length differences at points A, C, and D are 0.5λ, 1λ, and 0.5λ, respectively. These values can be used to analyze and predict the interference pattern observed at each point.