Question 16
Monochromatic light of
wavelength 690 nm passes through a diffraction grating with 300 lines per mm,
producing a series of maxima on a screen.
What is the greatest
number of maxima that can be observed?
A 4 B 5 C 8 D 9
Reference: Past Exam Paper – November 2012 Paper 12 Q30
Solution:
Answer: D.
For diffraction grating: d
sinθ = nλ
Slit separation, d = 1 / 300
= 3.33×10-3 mm = 3.33×10-6 m
Wavelength λ = 690×10-9 m
Let the maximum value for the angle θ from the central fringe be 90o on each side. {Note
that it is actually less – but we cannot have a value of θ being greater than
90o.}
d sinθ = nλ
Number of bright fringe in
one side, n = d sinθ / λ
n = d sinθ / λ = (3.33×10-6) sin 90 o / (690×10-9) = 4.8
That is, the 4th
bright fringe can be obtained but not the 5th bright fringe. We
cannot have 4.8 bright fringe. So, we can have up to 4 bright fringe on one
side.
We will also have 4 bright
fringe on the other side and one central fringe. These are also maxima.
Total number of fringes = 4 + 1 + 4 = 9
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