Answer to Question #150710 in Optics for R

Question

How many orders will be visible if the wavelength of the incident radiation is 4800 Å and the number of lines on the grating is 2500 lines per inch.

Answer 1

dsinθ = mλ . when λ = 90^o m = -m_max and m = m_max

where d is the diffraction grating line spacing, λ is the wavelength of the light source, θ is the

angle form the grating to the screen, and m = -m_max .... 0 ... m_max (integers)

We know that b + d  the maximum value of θ is 90⁰, that is sinθ = 1. Therefore, the number of orders visible with the granting is given as b + d = nλ

the grating is 2500 lines per inch.

m = $\frac{b + d}{λ}$

here b + d = 2500 lines per inch to 2.54 / 2500 to per cm

and λ = 5000$\dot{A}$ = 5000 * 10^-8cm

m = $\frac{2.54}{2500 * 4800 * 10^{-8}}$ = 21.6

m > 21

21 orders will be visible