Question

Problem 3: Double-slit experiment The monochromatic light diffracts on the two slits which are 0.1 mm apart (their size is negligible) and produces an interference pattern on the wall which is 3 m far from the apparatus.

a) The distance between the central bright fringe and the first off-center bright fringe is 2 cm. What is the wavelength of the light? Which color is it?

b) How many bright and dark fringes could we see on the wall?

c) We change the film with slits and the distance between adjacent dark fringe and bright fringe is 7 mm. What is the distance between two slits now?

Answer 1

Part a)

We know that the for young's double slit experiment, the position of n^th bright fringe is given by:

where, x is the distance of screen from slits = 3 m

lambda is the wavelength of light

d is the separation between slits = 0.1 mm

y_n is the distance of n^th bright fringe from the center.

So, according to question, y₁ - y₀ = 2 cm

The light is red in color.

Part b)

The m^th bright fringe can be given by:

since, the value of sine cannot be greater than 1:

m should be equal to 149.

So, total number of bright fringes will be equal to: 149 on either side + one central bright fringe = 149*2 + 1 = 299 bright fringes.

Also, number of dark finges: each drak fringe is surrounded by bright fringes, so total number of dark fringes = 299 - 1 = 298 dark fringes.

Part c)

We know the distance between adjacent dark or bright fringe: D

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