Yellow light of wavelength 590 nm is used in a double-slit interference experime

Question

Yellow light of wavelength 590 nm is used in a double-slit interference experiment in which the slits are each D 0.04 mm wide, d -0.18 mm apart, and L-1.30 m from a screen (a) What is the angle (in degrees) at which the first-order diffraction minimum is found? (b) There is an interference minimum at the same angle as the diffraction minimum you found in part (a). What is the order number (i.e. m value) of this minimum? If you wanted a narrower pattern on the screen, should you switch to red light or to violet light?

Explanation / Answer

part A :

use d sin theta = mL

L is wavelength

d is slit width

m is the order

theta is the angle

0.18 mm * sin theta = 1 * 590 *10^-9

sin theta = 0.032

theta = 0.187 deg

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part B : for interference minimum

(m+0.5) *590*10^-9= 0.18*10^-3 * sin 0.187

m = 1/2

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for narrower pattern Wave length be decreased so violet should be used

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