A diffraction grating has a lot of tiny parallel slits. The angle at which you f

Question

A diffraction grating has a lot of tiny parallel slits. The angle at which you find constructive interference can be determined using the same formula as with Young's Double Slit experiment. The one adjustment is that you need to convert the line density (number of lines per unit length) into the distance between adjacent slits (see the text).
Suppose you have a diffraction grating which has 300. lines/mm and you shine light with a wavelength of 431 nm through it. What is the angle at which you will observe the second order (m=2) bright fringe?

If the screen is 2.20 m away from the diffraction grating, what is the distance on the screen between the bright central and the second order bright fringe?

Explanation / Answer

We know,
d*Sin = m
where
is the wavelength
d is the separation of the slits or grating lines
m is the order of fringe.

d = 10^-3 / 300

d*Sin = m
10^-3/300 * Sin = 2 * 431*10^-9
Sin = 300 * 2*431*10^-6
= 15o
Angle at which you will observe the second order (m=2) bright fringe, = 15o

L = 2.20 m
y = Sin * L
y = sin(15) * 2.20
y = 0.569 m
Distance on the screen between the bright central and the second order bright fringe, y = 0.569 m

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