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प्रश्न
In Young's double slit experiment, show that:
`β = (λ"D")/"d"`
Where the terms have their usual meaning.
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उत्तर
Assume that S is a light source that is receiving light from another light source. Two line sources, S1 and S2, are equally spaced apart from light source S.
Let S1S2 = d
Path difference between waves at point P,
S2P - S1P = S2A
ΔS1S2A and ΔPCO are similar to each other.
∴ `("S"_2"A")/("S"_1"S"_2) =("OP")/("CP")`
Since CO is very much greater than S1S2,
So CP ≈ CO
∴ `("S"_2"A")/("S"_1"S"_2) = ("OP")/("CO")`
`("S"_2"A")/"d" = x/"D"`
∴ Path difference = `x/"D"`
For bright fringes, = mλ
`x = m ("D"λ)/"d"`
For mth and (m + 1)th fringe,
`x_m = m ("D"λ)/"d"` and
`x_(m + 1) = (m + 1) ("D"λ)/"d"`
Fringe width, `β = x_(m + 1) - x_m`
= `(m + 1) ("D"λ)/"d" - m ("D"λ)/"d"`
`β = ("D"λ)/"d"`
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In a Young's double slit interference experiment, the fringe pattern is observed on a screen placed at a distance D from the slits. The slits are separated by a distance d and are illuminated by monochromatic light of wavelength \[\lambda.\] Find the distance from the central point where the intensity falls to (a) half the maximum, (b) one-fourth the maximum.
Consider the arrangement shown in the figure. By some mechanism, the separation between the slits S3 and S4 can be changed. The intensity is measured at the point P, which is at the common perpendicular bisector of S1S2 and S2S4. When \[z = \frac{D\lambda}{2d},\] the intensity measured at P is I. Find the intensity when z is equal to
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(b) \[\frac{3D\lambda}{2d}\] and
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What should be the path difference between two waves reaching a point for obtaining constructive interference in Young’s Double Slit experiment ?
A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity:
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- Reason (R): The fringe width depends upon the wavelength of light (λ) used, the distance of the screen from the plane of slits (D) and slits separation (d).
What is fringe width?
What is the fringe width \(\beta\) in Young's double-slit experiment?
What is the angular fringe width \(\alpha\)?
