In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by 5 × 10^-2 m towards the slits, the change infringe width is 3 × 10^-5 m. If the distance between the slits is 10^-3 m, calculate the wavelength of light used.

Solution

Given,
Change in fringe width, $∆ β$ = 3 × 10^-5 m
Change in distance between the screen and slit, $∆ D$ = 5 × 10^-2 m
Distance between the slits, d = 10^-3 m

Fringe width, $β = \frac{λ}{d} D$
Therefore,
$∆ β = \frac{λ}{d} ∆ D$

$\Rightarrow$ $λ = d \frac{∆ β}{∆ D}$
$\Rightarrow$ $λ = 10^{- 3} \frac{3 \times 10^{- 5}}{5 \times 10^{- 2}} m = 6 \times 10^{- 7} m$

i.e., $λ = 6 \times 10^{- 7} \times 10^{10} Å = 6000 Å .$ is the wavelength of the light used in the experiment.

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Wave Optics

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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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

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.