Question

A diffraction grating with 600 lines/mm is illuminated with light of wavelength 510 nm. A very wide viewing screen is 2.6 m behind the grating.

What is the distance between the two m = 1 bright fringes?

How many bright fringes can be seen on the screen?

Answer 1

Solution:

Using the diffraction grating Formula :-

dsin = n

d = 1/(600*10^-3) = 1.666666667x10^-6 lines per meter.

(1.666666667*10^-6) sin = (1)(510x10^-9)

sin = 0.306

= 17.82°

TanΘ = opposite / adjacent
opposite = x
adjacent = 2.6m

Distance between the m=1 = 2x

Tan(17.82) = x/2.6

x= 0.836

Distance = 1.67 m

b) Max value of sin = 1
dsin = nλ
1.666666667*10^-6(1) = n(510*10^-9)
n = 3.2680
n = 3 ( you take the integer )
n is number of bright fringes in one half
Number of lines on two sides = 2x3 = 6 .
Now there is one fringe in the middle
So answer 6+1 = 7
Max bright fringes = 7 .

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