In a Young's double slit experiment, the separation between the slits is $0.15 m m$ . In the experiment, a source of light of wavelength $589 n m$ is used and the interference pattern is observed on a screen kept $1.5 m$ away. The separation between the successive bright fringes on the screen is:

Option 1 - <math> <mn>4.9</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math>

Option 2 - <math> <mn>6.9</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math>

Option 3 - <math> <mn>3.9</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math>

Option 4 - <math> <mn>5.9</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math>

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Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 4

Detailed Solution:

$\frac{Energy}{Volume} = \frac{{M L}^{2} T^{- 2}}{L^{3}} = ({M L}^{- 1} T^{- 2})$

The distance between two successive bright fringes is fringe width $(β)$ .

$β = \frac{λ D}{d} = \frac{589 * 10^{- 9} * 1.5}{0.15 * 10^{- 3}} = 5.9 m m$

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In Young’s double slit experiment the two slits are 0.6mm distance apart. Interference pattern is observed on a screen at a distance 80cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be__________nm.

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3d = 0.6mm

D = 80cm

= 800mm

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$\Rightarrow \frac{d y}{D} = (2 n + 1) \frac{λ}{2}$ [for Dark fringe at P]

n = 0, for first dark fringe

$\frac{d y}{D} = \frac{λ}{2}$

$λ = \frac{2 d}{D} y$

$= \frac{2 d}{D} \times \frac{d}{2} [y = \frac{d}{2}, G i v e n$ first dark fringe is observed on the screen directly opposite to one of the slits]

$λ = \frac{2 \times 0.6 \times 0.6}{800 \times 2}$

$λ = 450 m m$

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In a Young's double slit experiment, the separation between the slits is 0.15 m m . In the experiment, a source of light of wavelength 589 n m is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is: