cheechnchong
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Homework Statement
Light that has a wavelength of 668 nm passes through a slit 6.73 x 10^-6 m wide and falls on a screen that is 1.85 m away. What is the distance on the screen from the center of the central bright fringe in the third dark fringe on either side?
Homework Equations
I will discuss this in the attempt at the solution; however, my attempt will based on sin (theta) = m(wavelength/ width)
The Attempt at a Solution
I have drawn a diagram of what the problem basically states. Anyways...I first tried to find the angle between the length (1.85 m) and the area where the fringe resides (I called it X). So...my setup for the angle looks like this tan (theta) = x/1.85.
Then, knowing that sin(theta) is similar (~) to tan (theta) I proceeded to find the answer by setting up x/1.85 = 3 (668x10^-9 m/ 6.73 x 10^-6 m) and found that x = 0.55 m.
^I used this equation: sin (theta) = m(wavelength/ width). Just in case there is any confusion!
I am confused with the answer discrepensy from my book and my approach...the book has the solution 0.576 m for the bright fringe. I am not sure whether my approach is wrong OR that the discrepensy is fine...Please let me know - even if there is a mathematical error (which I don't think is the case).
I appreciate all the help I can Get!