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Question
Why are multiple colours observed over a thin film of oil floating on water? Explain with the help of a diagram.
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Solution
Interference due to a thin film:
The brilliant colours of soap bubbles and thin films on the surface of water are due to the interference of light waves reflected from the upper and lower surfaces of the film. The two rays have a path difference which depends on the point on the film that is being viewed. This is shown in above figure.
The incident wave gets partially reflected from upper surface as shown by ray AE. The rest of the light gets refracted and travels along AB. At B it again gets partially reflected and travels along BC. At Cit refracts into air and travels along CF. The parallel rays AE and CF have a phase difference due to their different path lengths in different media. As can be seen from the figure, the phase difference depends on the angle of incidence θ1, i.e., the angle of incidence at the top surface which is the angle of viewing, and also on the wavelength of the light as the refractive index of the material of the thin film depends on it. The two waves propagating along AE and CF interfere producing maxima and minima for different colours at different angles of viewing. One sees different colours when the film is viewed at different angles.
As the reflection is from the denser boundary, there is an additional phase difference of π radians (or an additional path difference λ). This should be taken into account for mathematical analysis.
RELATED QUESTIONS
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)
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.
Answer in brief:
In Young's double-slit experiment what will we observe on the screen when white light is incident on the slits but one slit is covered with a red filter and the other with a violet filter? Give reasons for your answer.
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?
Explain constructive and destructive interference with the help of a diagram?
How does wavefront division provide coherent sources?
Explain Young’s double-slit experimental setup and obtain the equation for path difference.
Does diffraction take place at Young’s double-slit?
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?
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?
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 ______
If the monochromatic source in Young's double slit experiment is white light, then ____________.
In a biprism experiment, D = 1 m, `lambda` = 6000 Å. When a convex lens is interposed between the biprism ru1d the eyepiece, then the distance between the images of the slits given by the Jens at two positions are 1.5 mm and 6.0 mm. The fringe width will be ______.
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 Young's double slit experiment the source is white light. One slit is covered with red filter and the other with blue filter. There shall be ____________.
The phenomenon of interference is based on ______.
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 identical light sources s1 and s2 emit light of same wavelength `lambda`. These light rays will exhibit interference if their ______.
`phi "and" phi_2 (phi_1 > phi_2)` are the work functions of metals A and B. When light of same wavelength is incident on A and B, the fastest emitted electrons from A are ____________ those emitted from B.
In the biprism experiment, the fringe width is 0.4 mm. What is the distance between the 4th dark band and the 6th bright band on the same side?
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 ______
Waves from two coherent sources of light having an intensity ratio I1 : I2 equal to 'x' interfere. Then in the interference pattern obtained on the screen, the value of (Imax - Imin)/(Imax + Imin) 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 ______.
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)
What is meant by Constructive interference?
Show graphically the intensity distribution in a single slit diffraction pattern.
In biprism experiment the maximum intensity is ‘I0’. If the path difference between the two interfering waves is ‘λ/4’ then intensity at the point on the screen is ______.
`[sin 45^circ = cos 45^circ = 1/sqrt 2]`
