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प्रश्न
Explain Young’s double-slit experimental setup and obtain the equation for path difference.
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उत्तर
Young’s double-slit experiment
- Wavefronts from S1 and S2 spread out and overlapping takes place to the right side of the double slit.
- When a screen is placed at a distance of about 1 meter from the slits, alternately bright and dark fringes which are equally spaced appear on the screen. These are called interference fringes or bands.
Equation for path difference: - Let d be the distance between the double slits S1 and S2 which act as coherent sources of wavelength λ.
- A screen is placed parallel to the double-slit at a distance D from it. The mid-point of S1 and S2 is C and the mid-point of the screen O is equidistant from S1 and S2. P is any point at a distance y from O.
- The waves from S1 and S2 meet at P either in-phase or out-of-phase depending upon the path difference between the two waves.
Young’s double-slit experimental setupδ = S2P – S1P
δ = S2P – MP = S2M -
The angular position of the point P from C is θ. ∠ OCP = θ.
- From the geometry, the angles ∠ OCP and ∠ S2S1M are equal.
∠ OCP = ∠ S2S1M = θ.
In right-angle triangle ∆ S1S2M, the path difference,
S2M = d sin θ
δ = d sin θ
If the angle θ is small, sin θ »tan θ θ
From the right angle triangle ∆ OCP,
tan θ = `"y"/"D"`
The path difference, δ = `"dy"/"d"`
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संबंधित प्रश्न
The intensity of the light coming from one of the slits in Young's experiment is twice the intensity of the light coming from the other slit. What will be the approximate ratio of the intensities of the bright and dark fringes in the resulting interference pattern?
What is interference?
Describe geometry of the Young’s double slit experiment with the help of a ray diagram. What is fringe width? Obtain an expression of it. Write the conditions for constructive as well as destructive interference.
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What is intensity (or) amplitude division?
The ratio of maximum and minimum intensities in an interference pattern is 36 : 1. What is the ratio of the amplitudes of the two interfering waves?
A thin transparent sheet is placed in front of a slit in Young's double slit experiment. The fringe width will ____________.
Band width for red light of wavelength 6600 Å is 0.42 mm. If red Light is replaced by blue light of wavelength 4400 Å, then the change m bandwidth will be ____________.
The distance between the first and ninth bright fringes formed in a biprism experiment is ______.
(`lambda` = 6000 A, D = 1.0 m, d = 1.2 mm)
In Young's experiment for the interference of light, the separation between the silts is d and the distance of the screen from the slits is D. If D is increased by 0.6% and d is decreased by 0.2%, then for the light of a given wavelength, which one of the following is true?
"The fringe width ____________."
In a Young's double-slit experiment, the intensity at a point where the path difference is `lambda/3` (`lambda` being the wavelength of the light used) is I. If I0 denotes the maximum intensity, then `"I"/"I"_0` is equal to ______.
In a double slit experiment, the two slits are 2 mm apart and the screen is placed 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?
Two sources of light 0.5 mm apart are placed at a distance of 2.4 m and wavelength of light is 5000 Å. The phase difference between the two light waves interfering on the screen at a point at a distance 3 mm from central bright band is ____________.
Two coherent light sources of intensity ratio 'n' are employed in an interference experiment. The ratio of the intensities of the maxima and minima in the interference pattern is (I1 > I2).
If two waves represented by `"y"_1 = 3 "sin" omega "t"` and `"y"_2 = 5 "sin" (omega "t" + pi/3)` interfere at a point, then the amplitude of the resulting wave will be about ____________.
The graph shows the variation of fringe width (β) versus distance of the screen from the plane of the slits (D) in Young's double-slit experiment Keeping other parameters the same. The wavelength of light used can be calculated as d = distance between the slits ______
Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive 90° out of phase is ______.
`[cos pi/2=0]`
A beam of electrons is used in Young's double-slit experiment. If the speed of electrons is increased then the fringe width will ______.
