Why is interference pattern not detected, when two coherent sources are far apart?
In Young’s experiment, the width of the fringes obtained with light of wavelength 6000 Å is 2.0 mm. Calculate the fringe width if the entire apparatus is immersed in a liquid medium of refractive index 1.33.

Solution

The fringe width will be very small (almost negligible) and fringes will not be separately visible if the separation between the two coherent sources is large.

Given,
Fringe width, $β$ = 2 mm
Wavelength of light used, $λ$ = 6000 $\overset{o}{A}$

Formula for fringe width in air, $β = \frac{Dλ}{d}$

Fringe width in liquid is, $β' = \frac{D λ'}{d} = \frac{D λ}{d μ}$

Refractive index of the medium, $μ = 1.33$ (given)

Therefore,
$β' = \frac{β}{μ}$

i.e., $β' = \frac{2.0}{1.33} = 1.5 mm .$

Some More Questions From Wave Optics Chapter

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Wave Optics

Why is interference pattern not detected, when two coherent sources are far apart?
In Young’s experiment, the width of the fringes obtained with light of wavelength 6000 Å is 2.0 mm. Calculate the fringe width if the entire apparatus is immersed in a liquid medium of refractive index 1.33.

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases:
Light diverging from a point source.

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For Daily Free Study Material Join wiredfaculty

Wave Optics

Why is interference pattern not detected, when two coherent sources are far apart?In Young’s experiment, the width of the fringes obtained with light of wavelength 6000 Å is 2.0 mm. Calculate the fringe width if the entire apparatus is immersed in a liquid medium of refractive index 1.33.

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases: Light diverging from a point source.

What is the shape of the wavefront in each of the following cases: Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Why is interference pattern not detected, when two coherent sources are far apart?
In Young’s experiment, the width of the fringes obtained with light of wavelength 6000 Å is 2.0 mm. Calculate the fringe width if the entire apparatus is immersed in a liquid medium of refractive index 1.33.

What is the shape of the wavefront in each of the following cases:
Light diverging from a point source.

What is the shape of the wavefront in each of the following cases:
Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.