1 Coherent light that contains two wavelengths 660 nm and 47

1. Coherent light that contains two wavelengths, 660 nm and 470 nm , passes through two narrow slits with a separation of 0.350 mm and an interference pattern is observed on a screen which is a distance 4.70 m from the slits.
Part A
What is the distance on the screen between the first-order bright fringe for each wavelength?
=m
2. Coherent light with wavelength of 598 nm passes through two very narrow slits and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe.
Part A
For what wavelength of light will the first-order dark fringe be observed at this same point on the screen?

= m

3. Young\'s experiment is performed with light of wavelength 502 nm from excited helium atoms. Fringes are measured carefully on a screen 1.20 m away from the double slit, and the center of the 20th fringe (not counting the central bright fringe) is found to be 10.6 mm from the center of the central bright fringe.
Part A
What is the separation of the two slits?
d= mm

Solution

Distance on the screen between the first-order bright fringe for each wavelength

= (lambda₁ - lambda₂) * R / d = (660 - 470) * 10^-9 * 4.70 / ( 0.350 * 10^-3 )

= 2.55 * 10^-3 m = 2.55 mm

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y = L lambda / d

0.00484 = 3 * 598 * 10^-9 / d

d = 0.00037066 m

0.00484 = 1/2 * 3 * lambda / 0.00037066

lambda = 1.19 mum