Advertisements
Advertisements
प्रश्न
A double-slit arrangement produces interference fringes for sodium light (λ = 589 nm) that are 0.20° apart. What is the angular fringe separation if the entire arrangement is immersed in water (n = 1.33)?
Advertisements
उत्तर
Given: θ1 = 0.20°, nw = 1.33
In the first approximation,
D sin θ1 = y1 and D sin θ2 = y2
`therefore (sin theta_2)/(sin theta_1) = "y"_2/"y"_1` ...(1)
Now, `y prop (lambdaD)/d`
For given d and D,
y ∝ λ
∴ `y_2/y_1 = lambda_2/lambda_1` ...(2)
Now, `n_w = lambda_1/lambda_2` ...(3)
From Eqs. (1), (2) and (3), we get
`(sin theta_2)/(sin theta_1) = lambda_2/lambda_1 = 1/n_w`
∴ `sin theta_2 = sin theta_1/n_w`
`sin theta_2 = (sin 0.2)/1.33`
`sin theta_2 = 0.0035/1.33`
sinθ2 = 0.0026
θ2 = sin−1 0.0026
θ2 = 9'
θ2 = 0.15°
This is the required angular fringe separation.
संबंधित प्रश्न
Write the important characteristic features by which the interference can be distinguished from the observed diffraction pattern.
Four light waves are represented by
(i) \[y = a_1 \sin \omega t\]
(ii) \[y = a_2 \sin \left( \omega t + \epsilon \right)\]
(iii) \[y = a_1 \sin 2\omega t\]
(iv) \[y = a_2 \sin 2\left( \omega t + \epsilon \right).\]
Interference fringes may be observed due to superposition of
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iv)
(d) (iii) and (iv)
A long narrow horizontal slit is paced 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1.0 m away from the slit. Find the fringe-width if the light used has a wavelength of 700 nm.
The intensity at the central maximum (O) in a Young’s double slit experimental set-up shown in the figure is IO. If the distance OP equals one-third of the fringe width of the pattern, show that the intensity at point P, would equal `(I_0)/4`.
Why are multiple colours observed over a thin film of oil floating on water? Explain with the help of a diagram.
Why two light sources must be of equal intensity to obtain a well-defined interference pattern?
What are coherent sources of light?
Obtain the relation between phase difference and path difference.
What is intensity (or) amplitude division?
What is a bandwidth of interference pattern?
Obtain the equation for bandwidth in Young’s double slit experiment.
In Young’s double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength λ0 = 750 nm and λ = 900 nm. What is the minimum distance from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other?
Light of wavelength 600 nm that falls on a pair of slits producing interference pattern on a screen in which the bright fringes are separated by 7.2 mm. What must be the wavelength of another light which produces bright fringes separated by 8.1 mm with the same apparatus?
In Young's double-slit experiment, if the width of the 2nd bright fringe is 4 x 10-2 cm, then the width of the 4th bright fringe will be ______ cm.
In Young's double-slit experiment, in an interference pattern, a second minimum is observed exactly in front of one slit. The distance between the two coherent sources is 'd' and the distance between source and screen is 'D'. The wavelength of the light source used is ______
A thin transparent sheet is placed in front of a slit in Young's double slit experiment. The fringe width will ____________.
Two identical light waves having phase difference 'Φ' propagate in same direction. When they superpose, the intensity of the resultant wave is proportional to ______.
A thin mica sheet of thickness 4 x 10-6 m and refractive index 1.5 is introduced in the path of the first wave. The wavelength of the wave used is 5000 A. The central bright maximum will shift ______.
The phenomenon of interference is based on ______.
In a biprism experiment, red light of wavelength 6500 Å was used. It was then replaced by green light of wavelength 5200 Å. The value of n for which (n + 1)th green bright band would coincide with nth red bright band for the same setting is ______.
In biprism experiment, the 4th dark band is formed opposite to one of the slits. The wavelength of light used is ______.
In the biprism experiment, a source of monochromatic light is used for a certain distance between slit and eyepiece. When the distance between two virtual sources is changed from dA to dB, then the fringe width is changed from ZA to ZB. The ratio ZA to ZB is ______
Light waves from two coherent sources arrive at two points on a screen with a path difference of zero and λ/2. The ratio of the intensities at the points is ______
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]`
In an interference experiment, the intensity at a point is `(1/4)^"th"` of the maximum intensity. The angular position of this point is at ____________.
(cos 60° = 0.5, `lambda` = wavelength of light, d = slit width)
A beam of electrons is used in Young's double-slit experiment. If the speed of electrons is increased then the fringe width will ______.
Show graphically the intensity distribution in a single slit diffraction pattern.
Interference fringes are produced on a screen by using two light sources of intensities I and 9I. The phase difference between the beams is `pi/2` at point P and π at point Q on the screen. The difference between the resultant intensities at point P and Q is ______.
The path difference between two interference light waves meeting at a point on the screen is `(87/2)lambda`. The band obtained at that point is ______.
A ray of light AO in a vacuum is incident on a glass slab at an angle of 60° and refracted at an angle of 30° along OB as shown in the figure. The optical path length of the light ray from A to B is ______.
