(596) Problem 4: A light with wavelength = 580 nm falls on a pair of closely sep

Question

(596) Problem 4: A light with wavelength = 580 nm falls on a pair of closely separated slits. The first dark fringe of the interference pattern is at an angle 6.75 degrees from the central maximum ©theexpertta.com 50% Part (a) Express the separation between the slits in terms of and p 50% Part (b) Solve for the numerical value of d in mm Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: 7 (5% per attempt) detailed view tanO JU in cotan) asin)acos atan)acotan) cosh cOS sinh) cotanh * 1 2 3 0 tanh o Degrees Radians BACKSPACE DEL CLEAR Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback.

Explanation / Answer

a) tan theta = y / D

d sin theta = (m + 1/2 ) * lambda

for m = 0, d sin theta = 1/2 * lambda

sin theta = lambda / 2 d

tan theta = lambda / 2 d

d = lambda / (2 * tan theta)

b) lambda = 580 nm, theta = 6.75 deg

d = (580 * 10-9) / (2 * tan 6.75)

d = 2.45 * 10-6 m = 2.45 mu.m

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