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## Physics library

### Course: Physics library>Unit 14

Lesson 2: Interference of electromagnetic waves

# Young's double slit equation

Let's derive a formula that relates all the variables in Young's double slit experiment as we explore Young's Double Slit Equation. Uncover how light's path length difference relates to the angle of incidence, and how this leads to constructive and destructive interference. Apply this knowledge to the world of wave patterns, trigonometry, and the wonders of diffraction! Created by David SantoPietro.

## Want to join the conversation?

• Why these two angles in video are equal? • David drew the first angle theta at a confusing point in this video. The angle theta should be redrawn away from the right angle (towards the left of the screen) from where it is now. If it is redrawn closer to the actual angle it represents in the triangle, one can see that two of the three right triangles are similar. Consequently, the angles are equal in these similar triangles.
• At we have a right triangle with one of the purple lines being the hypothenuse. How is it equal to the other purple side? Hypothenuse is the largest side, wouldn't we rather have to construct an isosceles triangle? •  I agree. So this is essentially the consequence caused by the assumption we've made, that we are assuming that the distance from the slits to the wall >>> (way greater than)distance between slits. So the triangle is very long and thin.( the diagram is not drawn to scale. If the diagram were to be drawn to scale, d would be invisible, and so the base of the long and thin right triangle.) So basically, because we are using very long and thin triangle, it "approaches" isosceles triangle so to speak. The assumption lets us use basic trig, so it's useful, and like David said, the assumption is a fairly reasonable one. Exactly. I had the same question!
• At
How on earth are the two angles equal? I've gone through all the answers on this page but am not satisfied! Help, please • First of all, if you measure these angles with a enough precision, they'll turn out to not be equal. However, they're very similar, and this can be shown with a real example. Suppose the 2 walls are 1,50 m apart, and the slits are 2,00 mm away from each other. If the point we're analyzing is 10,0 cm above the central axis (the central white line at the video), then we can easily find θ:
tan (θ) = 0.100/1.50 = 0.0667 , thus θ = 0.0666
Now let's find the angle x formed between the lower purple line and a line parallel to the central axis.
tan (x) = (0.100+0.001)/1.50 = 0.0673 , so x = 0.0672
To consider x = θ, we need to assume an error of 0.9% in our calculations, which is totally fine. (usually, errors can be even smaller by altering the initial conditions appropriately)
So, with x = θ, its easy to find that these two angles are equal, I encourage you to try it.
• At How did he equate the two angles, I see no connection between the angles to make them equal..? • what's going on at ? He's made a right triangle and said the long base and hypotenuse are the same length?? Shouldn't it be an isoceles? • How would you measure the angles? I mean, we're talking about a light wave, what experimental apparatus would you expect to use to get an angle formed by light? • he tells here hat light is always diffracting,so how does this happen?is it like 1 phone splits into another two?or is it that the photons spread out?if it is that then is there a limit to how much a light beam can diffract? • I think that the split needs to be wide enough for several photons to get through. Those which come through at the same time all have slightly different direction. And this difference in the direction of the momentum continues to be amplified over time/distance as it would have, had the electromagnetic wave not encountered the wll with slits. Hope that made sense :-)
• Could anyone please answer for me at , if that's a right angle, why are the top path and the remainder bottom path equal? • I struggled with this question as well. My understanding is that if the distance of the orange line is very small, then you can imagine the two lines almost being stack to each other. In other words, imagine if the orange line had a length of zero, then the lines must be the same. Anyway, that is how I made sense of it. There was a lot of handwaving in this demonstration, including how theta angles are congruent. Let me know what you think of my reasoning, not 100% if it is correct.  