Question

A.

Part 1A. Light of wavelength 640 nm is incident on a long narrow slit. Find the angle of the first diffraction minimum if the width of the slit is 1.5 mm. Answer in units of mrad.

Part 2A. Find the angle of the first diffraction minimum if the width of the slit is 0.15 mm. Answer in units of mrad.

B.

Part 1B. Monochromatic light from a helium-neon laser (wavelength 613.1 nm) is incident normally on a diffraction grating containing 4186 lines/cm. Find the angle at which the first-order maximum can be observed. Answer in units of ?

Part 2B. Calculate the angle at which the second-order maximum can be observed. Answer in units of ? .

Answer 1

A.

Part 1A) For first diffraction minimum,

dsin? = ?

=> ? = sin^-1(?/d) = sin^-1[(640 * 10^-9) / (0.15 * 10^-3)] = 4.27 mrad

Part 2A) ? = sin^-1(?/d) = sin^-1[(640 * 10^-9) / (1.5 * 10^-3)] = 0.427 mrad

B.

Part 1B) d = 1/4186 = 2.39 * 10^-4 cm = 2.389 * 10^-6 m

For first order maximum,

dsin? = ?

=> ? = sin^-1(?/d) = sin^-1[(613.1 * 10^-9) / (2.389 * 10^-6)] = 0.260 rad

Part 2B) For second order maximum,

dsin? = 2?

=> ? = sin^-1(2?/d) = sin^-1[(2 * 613.1 * 10^-9) / (2.389 * 10^-6)] = 0.539 rad