9702/May Jun/11/2011/Q27

A diffraction grating with 500 lines per mm is used to observe diffraction of monochromatic light of
wavelength 600 nm.

The light is passed through a narrow slit and the grating is placed so that its lines are parallel to
the slit. Light passes through the slit and then the grating.

An observer views the slit through the grating at different angles, moving his head from X parallel
to the grating, through Y, opposite the slit, to Z parallel to the grating on the opposite side.
How many images of the slit does he see?
A 3
B 4
C 6
D 7

Solution:
Answer: D

For diffraction grating: d sinθ = nλ

The largest value of θ is 90° on both sides of Y. We need to identify the largest order n for which an image can be seen (constructive interference).

There are 500 lines in 1×10^-3m.

Slit separation, d = (1×10^-3) / 500 m

Value of n = d sinθ / λ = (1×10^-3) (sin90°) / (500) (600×10^-9) = 3.33

Since n can only be an integer, the largest order is n = 3. So, there are 3 images on both sides of Y. An image will also be seen at Y, which is directly along the source.

Number of images = 3 + 3 + 1 = 7

Reference: PYQ - May/Jun 2011 Paper 11 Q27