Advertisements
Advertisements
प्रश्न
Answer in brief:
Explain what is the optical path length. How is it different from actual path length?
What is Optical Path length? How is it different from the actual Path length?
Advertisements
उत्तर १
Consider, a light wave with an angular frequency of w and a wave vector of k travelling in the x-direction through a vacuum. The phase of this wave is (kx - ωt). In a vacuum, light speed at c, but in a medium, it speeds at v.
k = `(2pi)/lambda = (2pi v)/(v lambda) = omega/v` as ω = 2πv and v = vλ, where v is the frequency of light.
If the wave travels a distance Δ x, its phase changes by Δ Φ = kΔx = ω Δx/v.
Similarly, if the wave is travelling in vacuum,
k = ω/c and Δ Φ = ω Δ x/c
Now, consider a wave travelling a distance Δ x in the medium, the phase difference generated is,
Δ Φ' = k' Δ x = ωn Δ x/c = ω Δ x'/c ...(1)
where Δ x' = n Δ x .....(2)
The distance nΔ x is called the optical path length of the light in the medium; it is the distance the light would have travelled in the same time t in vacuum (with the speed c).
The optical path length in a medium is the corresponding path in a vacuum that light traverses at the same time as it does in the medium.
Now, speed = `"distance"/"time"`
∴ time = `"distance"/"speed"`
∴ t = `"d"_"medium"/"v"_"medium" = "d"_"vaccum"/"v"_"vaccum"`
Hence, the optical path = `"d"_"vacuum"`
`= "v"_"vaccum"/"v"_"medium" xx "d"_"medium"`
`= "n" xx "d"_"medium"`
Thus, a distance d travelled in a medium of refractive index n introduces a path difference = nd - d = d (n - 1) over a ray travelling equal distance through vacuum.
उत्तर २
i. When a wave travels a distance Δx through a medium having a refractive index of n, its phase changes by the same amount as it would if the wave had travelled a distance nΔx in a vacuum.
ii. Thus, a path length of Δx in a medium of refractive index n is equivalent to a path length of nΔx in a vacuum.
iii. nΔx is called the optical path travelled by a wave.
iv. This means, the optical path through a medium is the effective path travelled by light in a vacuum to generate the same phase difference.
v. Optical path in a medium can also be defined as the corresponding path in a vacuum that the light travels at the same time as it takes in the given medium.
i.e., time = `"d"_"medium"/"v"_"medium" = "d"_"vacuum"/"v"_"vacuum"`
∴ `"d"_"vacuum" = "v"_"vacuum"/"v"_"medium" xx "d"_"medium" = "n" xx "d"_"medium"`
But `"d"_"vacuum"` = Optical path
∴ Optical path = n × `"d"_"medium"`
Thus, a distance d travelled in a medium of refractive index n introduces a path difference = nd - d = d(n - 1) over a ray travelling an equal distance through the vacuum.
संबंधित प्रश्न
Write the important characteristic features by which the interference can be distinguished from the observed diffraction pattern.
Write the necessary conditions to obtain sustained interference fringes.
State any one difference between interference of light and diffraction of light
Answer the following question.
Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double-slit experiment.
What is meant by coherent sources?
Describe Young's double-slit interference experiment and derive conditions for occurrence of dark and bright fringes on the screen. Define fringe width and derive a formula for it.
What are the two methods for obtaining coherent sources in the laboratory?
Two coherent sources whose intensity ratio is 25:1 produce interference fringes. Calculate the ratio of amplitudes of light waves coming from them.
Draw a neat labelled ray diagram of the Fresnel Biprism experiment showing the region of interference.
What is intensity (or) amplitude division?
How do source and images behave as coherent sources?
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.
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 ______.
In interference experiment, intensity at a point is `(1/4)^"th"` of the maximum intensity. The angular position of this point is at (sin30° = cos60° = 0.5, `lambda` = wavelength of light, d = slit width) ____________.
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).
In biprism experiment, if the 5th bright band with wavelength 'λ1' coincides with the 6th dark band with wavelength 'λ2' then the ratio `(lambda_2/lambda_1)` is ______
In Young's double slit experiment, for wavelength λ1 the nth bright fringe is obtained at a point P on the screen. Keeping the same setting, source of light is replaced by wavelength λ2 and now (n + 1)th bright fringe is obtained at the same point P on the screen. The value of n is ______.
A double slit experiment is immersed in water of refractive index 1.33. The slit separation is 1 mm, distance between slit and screen is 1.33 m. The slits are illuminated by a light of wavelength 6300 Å. The fringe width is ______.
In Young's double-slit experiment, the distance between the slits is 3 mm and the slits are 2 m away from the screen. Two interference patterns can be obtained on the screen due to light of wavelength 480 nm and 600 run respectively. The separation on the screen between the 5th order bright fringes on the two interference patterns is ______
If we have two coherent sources S1 and S2 vibrating in phase, then for an arbitrary point P constructive interference is observed whenever the path difference is ______.
How will the interference pattern of Young's double slit change if one of the two slits is covered by a paper which transmits only half of the light intensity?
The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio `("I"_"max" - "I"_"min")/("I"_"max" + "I"_"min")` is `5/x`. Then the value of x will be equal to ______.
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 ______.
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 ______.
