Plane electromagnetic waves of wavelength = 633 nm (red light) from a helium-neo

Question

Plane electromagnetic waves of wavelength = 633 nm (red light) from a helium-neon laser are incident horizontally from the left on an opaque vertical screen having two narrow slit-shaped openings separated by a distance d = 0.104 mm.  Light emerging from the two slits forms an interference pattern on a second vertical screen located a distance l = 95.5 cm away. Maximum brightness is observed at the center of the pattern, at a height midway between the two slits. Above that, what is the angle at the first minimum in brightness, i.e. at the center of the first dark fringe?

a.0.697 deg

b.6.09 X 10-3 deg

c.0.349 deg

d.0.174 deg

e.3.04 X 10-3 deg -- this is not correct

Above the first dark fringe, what is the angle at the next maximum in brightness above the central maximum?

a.0.349 deg

b.0.174 deg -- this is not correct

c.6.09 X 10-3 deg

d.0.697 deg

e.3.04 X 10-3 deg

What is the vertical distance above a height midway between the two slits to the second minimum in brightness?

Above the first dark fringe, what is the angle at the next maximum in brightness above the central maximum?

a.0.349 deg

b.0.174 deg -- this is not correct

c.6.09 X 10-3 deg

d.0.697 deg

e.3.04 X 10-3 deg

Explanation / Answer

part 1 )

dsintheta = m*lambda

m =1

theta = sin^-1(lambda/d)

lambda = 633 nm

d = 0.104 mm

theta = 0.349 degree

part b )

now m = 2

theta = sin^-1(2lambda/d )

theta = 0.697 degree

part c )

for destrcutive interference

dsintheta = (m+1/2)lambda

m = 1

tan thet = y/D

theta is small so tan theta = sin theta

y = (m+1/2) * lambda*D/d

y = 8.72 x 10^-3 m

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