A diffraction grating casts a pattern on a screen located a distance L from the

Question

A diffraction grating casts a pattern on a screen located a distance L from the grating. The central bright fringe falls directly in the center of the screen. For the highest-order bright fringe that hits the screen, m=x, and this fringe hits exactly on the screen edge. This means that 2x+1 bright fringes are visible on the screen.

(a) What happens to the number of bright fringes on the screen if the wavelength of the light passing through the grating is doubled? Suppose that x is an even number.

(b) What happens to the number of bright fringes on the screen if the wavelength of the light passing through the grating is doubled? Suppose that x is an odd number.

(c) What happens to the number of bright fringes on the screen if the spacing d between adjacent slits is doubled?

Explanation / Answer

here,

From Young's slit experiment,

m = Y*d/Lamda*L ---------------------(1)

Where,
Y = displacement for bright fringe
d = Slit seperation
Lamda = Wavelength
L = Distance to screen

also
no of fringes = 2x + 1, Where, x = m
so, n = 2m+1-------------------------------(2)

A) if Lamda is doubled, M is halfed, then n = x + 1

B) same as part a.

C) if d is doubled , m will be doubled (Eqn 1)

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