Plane electromagnetic waves of wavelength lambda = 515 nm (green light) from a l

Question

Plane electromagnetic waves of wavelength lambda = 515 nm (green light) from a laser diode are 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 times 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 unelected light beam. What is the angle theta of the first maximum in brightness below the central maximum? 51 deg 0.51 deg 36 deg 39 deg 31 deg A circular lens of diameter 4.0 cm is used to image very small, closely spaced powder granules with 540 nm illumination. Using the Rayleigh criterion for the diffraction limit of resolution, compute the smallest angular separation in radians for two granules to be just barely resolvable as distinct. 1.3 times 10^-5 rad 1.1 times 10^-5 rad 9.2 times 10^-4 rad 7.5 times 10^-4 rad 1.6 times 10^-5 rad

Explanation / Answer

Question 15:

lambda = 515 nm

d = 1.00*10-6 m

For diffraction grating, n = 1 for 1st maximum;

d sin e = n*lambda

sin e = 1*515*10-9 m / 1.00*10-6 m = 0.515

e = 30.9975

e = 31 deg

Hence, Option 'e' is the Correct Choice.

Question 16:

According to Raleigh's criterion,

sin e = 1.22* lambda/d

given, lambda = 540 nm; Diameter of the lens, d = 4 cm.

sin e = 1.22*540*10-9/4*10-2 = 1.647*10-5

e = 1.6*10-5

Hence, Option 'e' is the Correct Choice.

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