Are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 bright fringes/cm on the screen, what is the wavelength of the monochromatic light

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Question:

A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 bright fringes/cm on the screen, what is the wavelength of the monochromatic light?

Given Information:

Distance from the double slits to the screen = D = 4.8 m

Double slit separation distance = d = 1.8 mm = 0.0018 m

Number of fringes = m = 5

Distance between fringes = y = 1 cm = 0.01 m

Required Information:

Wavelength of the monochromatic light = λ = ?

Wavelength of the monochromatic light = λ = 7.5x10⁻⁷ m

Explanation:

The wavelength of the monochromatic light can be found using young's double slits formula,

λ = yd/mD

where d is the double slit separation distance, D is the distance from the double slits to the screen, y is the distance between bright fringes and m is number of fringes.

λ = 0.01*0.0018/5*4.8

λ = 0.00000075 m

λ = 7.5x10⁻⁷ m

Therefore, the wavelength of the monochromatic light is 7.5x10⁻⁷ m

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