Question

# Two slits spaced 0.130 mm apart are placed 90.0 cm from a screen and illuminated by...

Two slits spaced 0.130 mm apart are placed 90.0 cm from a screen and illuminated by coherent light with wavelength 550 nm. The intensity at the center of the central maximum is 4.30 × 10-6 W/m2. What is the distance on the screen between the third bright fringe and the sixth dark fringe? What is the intensity at a point midway between the center of the central maximum and the first minimum?

given separation is d = 0.13 mm

= 130 X 10-6 m

= 550 nm = 550 X 10-9 m

Io = 4.30 X 10-6 W/m2

D = 90 cm = 0.9 m

the distance on the screen between the third bright fringe and the sixth dark fringe is " Y "

Y = D / 2 d

Y = 550 X 10-9 X 0.9 / 2 X 130 X 10-6

Y = 1.90 X 10-3 m

the distance on the screen between the third bright fringe and the sixth dark fringe is Y = 1.90 X 10-3 m

then next

the path difference is " dx "

dx = ( Y/2 ) d / D

dx = Y d / 2 D

dx = 1.9 X 10-3 X 130 X 10-6 / 2 X 0.9

dx = 1.372 X 10-7 m

then phase difference = 360 X dx /

= 360 X 1.372 X 10-7 / 550 X 10-9

= 89.8 or nearly 90o

using equation

I = Io cos2 (/2)

I = 4.3 X 10-6 X cos2 45

the intensity at a point midway between the center of the central maximum and the first minimum is

I = 2.15 X 10-6 W/m2

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