Question

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?

Answer 1

given separation is d = 0.13 mm

= 130 X 10^-6 m

= 550 nm = 550 X 10^-9 m

I_o = 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 90^o

using equation

I = I_o 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