Sodium light of wavelength 589 nm is incident normally on a grating having 3000 lines per centimeter. What is the highest order of the spectrum obtained with this grating? (Ans: 5th)



Data Given:


Wavelength of light = λ = 589 nm = 589 ｘ 10⁻⁹ m

N = 3000 L cm⁻¹ = 300000 L m⁻¹

Angle = Î¸ = 90° 


To Find:


Order of spectrum = m = ?

Solution:


Using the following formula 

d sin Î¸ = m Î»

or 

m = `\frac {d sin θ}{λ}`

where d = `\frac {1}{N}` So,

m = `\frac {sin θ}{Nλ}`

by putting values of Î», θ, and N

m = `\frac {sin 90°}{176700000 ｘ 10⁻⁹ }`

m = `\frac {1}{1.767ｘ 10⁸ ｘ 10⁻⁹ m }`

m = `\frac {1}{0.1767}`

or

m = 5.66

or

m = 5th -------------Ans.

Thus the highest order spectrum obtained is 5th.



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