Calculate the wavelength of light illuminates two, slits 0.5 mm apart and produces an interference pattern on a screen placed 200 cm away from the slits. The first bright fringe is observed at distance of 2.4 mm from the central bright image. (Ans: 600 nm)



Data Given:


Separation between the slits = d = 0.5 mm = 0.5 ｘ 10⁻³ m = 5.0 ｘ 10⁻⁴ m 

Distance between Slit and screen = L = 200 cm = 2 m

Distance between the adjacent Maxima on the screen = y = 2.4 mm = 2.4 ｘ 10⁻³ m 

Order (1st Minimum) = m = 1


To Find:

Wavelength of light = λ = ?



Solution:


Now using formula for `\m_{th}` bright fringe 

y = `\frac {m λ L}{d}`

or

λ = `\frac {y d}{mL}`

by putting values

λ = `\frac {2.4 ｘ 10⁻³ m ｘ 5.0 ｘ 10⁻⁴ m}{1 ｘ 2 m}`

λ = `\frac {12 ｘ 10⁻⁷ m² }{2 m}`

λ = 6 ｘ 10⁻⁷ m 

or

λ = 600 ｘ 10⁻⁹ m

or

λ = 600 nm  ------------Ans




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