1Two slits spaced 0450 mm apart are placed 780 cm from a scr

1.Two slits spaced 0.450 mm apart are placed 78.0 cm from a screen.
Part A
What is the distance between the second and third dark lines of the interference pattern on the screen when the slits are illuminated with coherent light with a wavelength of 530 nm ?
y= mm

2.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

Solution

1. d = 0.45 mm = 0.450 x 10^-3 m

lambda = 530nm = 530 x 10^-9 m

D = 78 cm = 0.78 m

for mth dark fringe,

y = (m + 0.5)* lambda *D / d

for m = 2

y2 = 2.5*lambda*D / d

for m = 3

y3 = 3.5*lambda*D/d

y3 - y2 = lambda*D /d = (530 x 10^-9 x 0.78) / (0.45 x 10^-3)

deltaY = 0.92 x 10^-3 m = 0.92 mm

2. delta Y = (m + 0.5) * (lambda1 -lambda2) * D / d

    = (0.5 x (660 - 470) x 10^-9 x 4.70 ) / (0.350 x 10^-3)

     = 1.276 x 10^-3 m