Monochromatic light of wavelength 690 nm passes through a diffraction grating with 300 lines per mm, producing a series of maxima on a screen.

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 90^o on each side. {Note that it is actually less – but we cannot have a value of θ being greater than 90^o.}

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 4^th bright fringe can be obtained but not the 5^th 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