Light with a wavelength of 560.0 nm is incident on a pair of slits with a separation of 0.380 mm. (a) Find the angles corresponding to the locations of the first three orders of bright fringes away from the central bright fringe

Angles corresponding to the locations of the first three orders of bright fringes away from the central bright fringe are;

∅₁ = 0.8439°

∅₂ = 0.1688°

∅₃ = 0.2533°

Explanation:

Given that;

wavelength λ = 560 nm = 560 × 10⁻⁹

Separation between slits d = 0.380 mm = 0.00038

n = first three orders = 1st order, 2nd order and 3rd oder.

we know that for constructive interference;

λn = dsin∅

sin∅ = λn/d

∅ = sin⁻¹ ( λn/d )

where λ is wavelength, ∅ is the angle, d is the distance between slits, n is the order of constructive interference.

now;

-First order;  n = 1

∅₁ = sin⁻¹(λn/d) = sin⁻¹( (560 × 10⁻⁹)×(1) /0.00038 )

∅₁ = sin⁻¹( 0.001473) = 0.8439°

-2nd order;  n = 2

∅₂ = sin⁻¹(λn/d) = sin⁻¹( (560 × 10⁻⁹)×(2) /0.00038 ) =

∅₂ = sin⁻¹( 0.002947) = 0.1688°

-3rd order;  n = 3

∅₃ = sin⁻¹(λn/d) = sin⁻¹( (560 × 10⁻⁹)×(3) /0.00038 ) =

∅₃ = sin⁻¹( 0.004421) = 0.2533°

Therefore, angles corresponding to the locations of the first three orders of bright fringes away from the central bright fringe are;

∅₁ = 0.8439°

∅₂ = 0.1688°

∅₃ = 0.2533°

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