Blue light of wavelength 480 nm illuminates a diffraction grating. The second order image is formed at an angle of 30° from the central image. How many lines in a centimeter of the grating have been ruled? (Ans: 5.2ｘ10³ lines per cm)



Data Given:


Wavelength of light = λ = 480 nm = 480 ｘ 10⁻⁹ m

Angle = θ = 30° 

Order of spectrum = m = 2


To Find:


Number of lines per cm = N = ?

Solution:


Using the following formula 

d sin θ = m λ

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

`\frac {1}{N}` sin θ = m λ

or

N = `\frac { sin θ}{m λ}`

by putting the corresponding values 

N = `\frac {sin 30° }{2 ｘ480 ｘ 10⁻⁹ m}`

N = `\frac {0.5 }{960 ｘ 10⁻⁹ m}`

N = 5.208 ｘ 10⁵ lines per meter

or

N = 5.208 ｘ 10³ lines per cm  -------------Ans.






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