How does the fringe width of interference fringes change, when the whole apparatus of young’sexperiment is kept in liquid of refractive index 1.3 ?
Question
How does the fringe width of interference fringes change, when the whole apparatus of young’sexperiment is kept in liquid of refractive index 1.3 ?
Solution
The fringe width of interference fringes in Young's experiment changes when the whole apparatus is kept in a liquid of refractive index 1.3.
To understand how the fringe width changes, we need to consider the effect of the liquid on the interference pattern.
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First, let's recall the setup of Young's experiment. It consists of a source of coherent light, a barrier with two slits, and a screen where the interference pattern is observed.
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When the experiment is conducted in air or vacuum, the interference pattern is formed due to the superposition of light waves from the two slits. The fringe width is determined by the wavelength of light and the distance between the slits and the screen.
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However, when the whole apparatus is immersed in a liquid with a refractive index of 1.3, the speed of light changes. The refractive index is defined as the ratio of the speed of light in vacuum to the speed of light in the medium.
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As the speed of light changes in the liquid, the wavelength of light also changes. This means that the fringe width will be affected.
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The change in fringe width can be calculated using the formula:
Δy = λ * D / d
where Δy is the change in fringe width, λ is the wavelength of light, D is the distance between the slits and the screen, and d is the distance between the slits.
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Since the refractive index of the liquid is 1.3, the wavelength of light in the liquid will be λ' = λ / 1.3.
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Substituting this value into the formula, we can calculate the new fringe width in the liquid:
Δy' = λ' * D / d = (λ / 1.3) * D / d
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Therefore, the fringe width in the liquid will be smaller than the fringe width in air or vacuum. This is because the wavelength of light in the liquid is shorter, leading to a narrower interference pattern.
In conclusion, when the whole apparatus of Young's experiment is kept in a liquid of refractive index 1.3, the fringe width of interference fringes decreases.
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