Question

(a) In a biprism experiment the micrometer reading for zero order and tenth order fringes are 1.25 mm and 2.37 mm respectively when light of X = 5.90 x 10-5 cm. is used. Now what will be the position of zero order and tenth order fringes if X is changed to 7.50 x 10-5 cm.​

Answer 1

Answer:

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Answer 2

Given:

The micrometer reading for zero-order fringe= 1.25 mm

The micrometer reading for tenth order fringe = 2.37 mm

The wavelength of the light used = 5.90 X 10⁻⁵cm

To Find:

The position of zero-order and tenth-order fringes if wavelength used is 7.50X 10⁻⁵cm.

Solution:

Since the reading of the micrometer for zero-order is non-zero,

⇒ There is a zero error which is equal to = 1.25 mm

The zero error needs to be removed to find the true positions of the fringes.

The distance between zero-order and 10th order fringe = y10 = 2.37mm−1.25mm

=1.12mm

The position of nth order fringe = yn=nλD / d

Here, n= order of the fringe

λ = wavelength of the light used

D = Distance between the source and the screen

d= distance between the slits

Since D and d are constants (setup used is same),

⇒ Δyn / yn = Δλ / λ

Substituting Δλ  = 7.50X 10⁻⁵cm - 5.90 X 10⁻⁵cm = 1.60 X 10⁻⁵cm, λ=5.90 X 10⁻⁵cm

Δyn = 0.27 yn

⇒ y′n = yn + Δyn

     =yn + 0.27 yn = 1.27 yn

So for n = 10, y'10 = 1.27 X 1.12 = 1.42mm

Adding the zero error of the micrometer gives the new position of 10th order fringe = 1.25 + 1.42 = 2.67mm

Since n = 0 for the zero-order fringe, its position remains the same.

Hence, the new position of the zero-order and the 10th fringe will be 1.25mm and 2.67mm respectively.