Two thin parallel slits that are 1.00×10 2 mm apart are illuminated by a laser b

Question

Two thin parallel slits that are 1.00×102 mm apart are illuminated by a laser beam of wavelength 580 nm .

Part A

On a very large distant screen, what is the total number of bright fringes (those indicating complete constructive interference), including the central fringe and those on both sides of it? Solve this problem without calculating all the angles! (Hint: What is the largest that sin can be? What does this tell you is the largest value of m?)

Part B

At what angle, relative to the original direction of the beam, will the fringe that is most distant from the central bright fringe occur?

Explanation / Answer

We know that
(a)

dSin(angle) = n*lambda(wavelength)
For maximum angle Sin(angle) = 1
d = n*Lambda
n = d/Lambda = (1*10-2*10-3)/(580*10-9) = 17.24
so approx 17 we can say fringes will formed at one side
So on both side = (2*17) + 1 = 35 fringes

(b) Sin(angle) = (n*Lambda)/d = (17*580*10-9)/(10-5)
Angle = 80.401 degree.

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