The first order maximum due to a grating when using blue light of wavelength 376

Question

The first order maximum due to a grating when using blue light of wavelength 376 nm is at 19.8 degrees.

a) What is the slit separation in mm for this grating?

b) What are the number of lines/mm in this grating?

c) What is in meters the position y1 on the screen, relative to the central maximum of that same first order maximum if the viewing screen is located 0.40 m to from the slits?

d) What is then in meters the position y2 on the screen, relative to the central maximum of the second order maximum?

Explanation / Answer

(a)

from the diffraction formula

d sin theta = m L

d = mL/sin theta

= 1 ( 376 nm)/ sin 19.8

= 1.11 * 10 ^-6 m

(b)

N = 1/d = 1/ 1.11 * 10 ^-6 m = 900.9 lines/mm

(c)

y = m ( lamda) L/d

   = 1 ( 376 nm) ( 0.40 m)/1.11 * 10 ^-6 m

=0.135 m

(d)

y = m ( lamda) L/d

   = 2 ( 376 nm) ( 0.40 m)/1.11 * 10 ^-6 m

=0.270 m

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