I don't know where you got sin theta = .1 from??
Look if I use m = 0
and the formula I used then I get L = 500m
when I do arctan(25/500) I get 2.86 degrees.
The sin theta = .1 is a typo
Yes, I got 2.87 degrees in the line above.
Can you also explain to me why it would be m=0 and not m=1?
Thank you so much for all the help!
I got L = 500 from
y'm = (m+1/2) (lamda L/d)
25 = (0 + 1/2) (5L/50)
L = 500
m = 0 because it asked for the first destructive interference. Interference happens when m = 0, +/-1 , +/-2, +/-3 ....etc
m=0 is the first time that the waves arrive half a wavelength apart.
d sin theta = (1/2) lambda
when m = 0
Ok. I see what you did. It is not really a two source interference problem although the effect is the same.
It seems like you're referring to the calculation of an angle using the arctan function. Let me explain how to calculate the angle step by step.
First, you mentioned using the equation L = m * 500, where L represents the length and m represents the slope. Assuming m in this case is 0, which means there is no slope, we can substitute m = 0 into the equation:
L = 0 * 500
L = 0
So, in this case, the length L is 0.
Next, you mentioned using the arctan function to find an angle. Specifically, you used the arctan function with the argument 25/500. This suggests that you're trying to calculate an angle related to a right triangle.
To clarify, the arctan function calculates the inverse tangent of an angle. In other words, it helps us find the angle whose tangent is a given value. In this case, you used arctan(25/500).
If we plug in these values into a calculator, we can find that arctan(25/500) is approximately 0.0507 radians or about 2.906 degrees. However, this angle does not appear to be related to your initial question about sin theta = 0.1. So, it seems there might be some confusion in the context of your question.
If you can provide additional details or clarify your question, I'll be happy to assist further.