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 = θ = 90° 


To Find:


Order of spectrum = m = ?

Solution:


Using the following formula 

d sin θ = m λ

or 

m = dsinθλ

where d = 1N So,

m = sinθNλ

by putting values of λ, θ, and N

m = sin90°176700000ｘ10⁻⁹

m = 11.767ｘ10⁸ｘ10⁻⁹m

m = 10.1767

or

m = 5.66

or

m = 5th -------------Ans.

Thus the highest order spectrum obtained is 5th.



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