Plane electromagnetic waves of wavelength = 500 nm (green light) from a high pow
ID: 1439621 • Letter: P
Question
Plane electromagnetic waves of wavelength = 500 nm (green light) from a high power laser diode is incident horizontally from the left on a vertically oriented diffraction grating having 10,000 slits per centimeter, i.e. a slit separation of d = 1.00 X 10-6 m. Light emerging from the slits of the grating forms an interference pattern on a vertical screen to the right. Maximum brightness is observed at the center of the pattern, corresponding to an undeflected light beam. What is the angle of the first maximum in brightness below the central maximum?
a.
30.0 deg
b.
0.589 deg
c.
0.500 deg
d.
36.1 deg
e.
39.3 deg
What is the angle of the second maximum in brightness below the central maximum?
39.3 deg
45.0 deg
36.1 deg
90.0 deg
30.0 deg
a.39.3 deg
b.45.0 deg
c.36.1 deg
d.90.0 deg
e.30.0 deg
Explanation / Answer
here,
lamda = 500 nm = 5*10^-7 m
d = 10^-6 m
Part A:
From Diffraction experiment,
SinA = m*Lamda/d
A = arcSin(m*lamda/d)
A = arcSin(1*5*10^-7/10^-6)
A = 30 degrees
Part B:
second maxima, m = 2
A = arcSin(m*lamda/d)
A = arcSin(2*5*10^-7/10^-6)
A = 90 degrees