A laser beam of wavelength 670 nm shines through a diffraction grating that has 750 lines/mm. Sketch the pattern that appears on
a screen 1.0 m behind the grating, noting distances on your drawing and explaining where these numbers come from.
1 answer:
Answer:
only first order exist with vertical distance of y = 0.58 m from central order
Explanation:
Given:
- The wavelength of laser beam λ = 670 nm
- Diffraction grating N = 750 lines/mm
- Distance of screen from grating x = 1.0 m
Find:
Sketch the pattern that appears on a screen 1.0 m behind the grating, noting distances on your drawing and explaining where these numbers come from.
Solution:
- We will use the results derived from Young's experiment that relates the position of the fringes relative to central order depending on the wavelength of the incident light as follows:
sin(Q) = m* λ*N m = 0, 1, 2, 3, ....
- We will find the first order of bright fringe @ m = 1:
Q_1 = sin^-1 ( 670*750*10^-6)
Q_1 = 0.53 radians
- The vertical distance from the central order is:
y_1 = x*tan(Q_1)
y_1 = 1.0*tan(0.53)
y_1 = 0.58 m
- Re-do the calculations for m = 2:
Q_2 = sin^-1 (2* 670*750*10^-3)
Q_2 = sin^-1 ( > 1)
Q_2 = does not exist
- Hence the second order is too far apart and does on exist in our case. So we have a pair of bright fringe above ans below the central order displaced @ 0.58 m. (See attachment for sketch)
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