91Ó°ÊÓ

Given a red line and a green line of the same order in the pattern produced by a diffraction grating. Gating spacing $d$ is increased.

Half-width of any other line depends on its location relative to the central axis and is

$\mathrm{Δ}{\mathrm{θ}}_{hw}=\frac{\mathrm{λ}}{Nd\cos \mathrm{θ}}$(half-width of the line )

Here,$\mathrm{λ}$ is wavelength

d is ruling separation.

N is number of rulings

The dispersion of a grating at an angle is given by

$\frac{\mathrm{Δ}\mathrm{θ}}{\mathrm{Δ}\mathrm{λ}}=\frac{m}{d\cos \mathrm{θ}}$

Here, m is order,

d is grating space and

$\mathrm{Δ}\mathrm{λ}$is wavelength difference.

The path length difference is

localid="1663139636669" $d\sin \mathrm{θ}=m\mathrm{λ}$, for $m=0, 1, 2, ...$(maxima lines)

Here $\mathrm{λ}$is wavelength.

The half-width of any other line depends on its location relative to the central axis and is

$\mathrm{Δ}{\mathrm{θ}}_{hw}=\frac{\mathrm{λ}}{Nd\cos \mathrm{θ}}$(half the width of the line )

Here, half-width is inversely related to grating spacing d.

So if the grating space increases, half the width decreases.

The dispersion of a grating at an angle is given by

$\frac{\mathrm{Δ}\mathrm{θ}}{\mathrm{Δ}\mathrm{λ}}=\frac{m}{d\cos \mathrm{θ}}$

Separation of lines is inversely related to grating space, so

So if the grating space increases, the separation of the lines decreases.

The path length difference is

$d\sin \mathrm{θ}=m\mathrm{λ}$

Since the grating spacing d increases, the path length difference also increases, so lines will shift to the right.