Young’s Experiment(Introduction)
Young’s experiment, the classical investigation into the nature of light, an investigation that provided the basic element in the development of the wave theory and was first performed by the English physicist and physician Thomas Young in 1801. In this experiment, Young identified the phenomenon called interference. Observing that when light from a single source is split into two beams, and the two beams are then recombined, the combined beam shows a pattern of light and dark fringes, Young concluded that the fringes result from the fact that when the beams recombine their peaks and troughs may not be in phase (in step). When two peaks coincide they reinforce each other, and a line of light results; when a peak and a trough coincide they cancel each other, and a dark line results.
YOUNG’S EXPERIMENT
The British physicist Thomas Young used an ingenious technique to make a coherent source of wave emanating from s1 and s2.
He made two pinholes s1 and s2 very close to each other on an opaque screen. These were illuminated by another pinhole that was in turn, lit by a bright source. Light waves spread out from S and fall on both s1 and s2.
s1 and s2 then behave like two coherent sources because light waves coming out from s1 and s2 are derived from the same original source.
Now spherical wave emanating from s1 and s2 will produce interference fringes on the screen GG’ as shown in fig. Let separation between s1 and s2 is d. The wavelength of wave is and the perpendicular distance between slits and screen is D.
Consider a point P on the screen at a distance x from C. The path difference between the waves from s1 and s2 arriving at P is
The waves from S1 and S2 arriving at a point on the screen will interfere constructively or destructively depending upon this path difference.
POSITION OF BRIGHT FRINGES:-
Here, Path difference=
This is the distance of the bright fringes from C
( distance of central bright fringe from C)
(first bright fringe)
(second bright fringe)
……………………………..
……………………………..
(nth bright fringe)
POSITION OF DARK FRINGES:-
Here, Path difference=
This is the distance of the dark fringes from C
( distance of first dark fringe from C)
(second dark fringe)
(third dark fringe)
……………………………..
……………………………..
( nth dark fringe)
FRINGE WIDTH
The distance between two consecutive bright or dark fringes is called fringe width, denoted by .
Dark fringe width is also the same
The angular width of a fringe is given by
The angular width of a fringe is independent of the position of the screen.
NOTE:-
(1) the Locus of the point P laying in the x-y plane, such that is a constant, is a hyperbola. If the distance D is very large compared to the fringe width, the fringe will be a very nearly straight line.
(2) In the double-slit experiment, if the source S is slightly away from the perpendicular bisector with some angle, then the central bright fringe occurs at the same angle, on the other side. It is because the paths travelled by rays SAO and SBO are equal.in 2nd fig the path of the rays S’AO” and S”BO” are equal.
(3) we should mention here the fringes are straight lines although S1 and S2 are point source or thin slit but in case of slits, fringe is more intense.
(4) If the source is moved nearer the double slits, the fringe width is unaffected. but the intensity of fringes increases.
(5) If one of the slits is covered up, the fringes disappear. This shows that the interference pattern is due to the superposition of two coherent light waves.
(6) When the apparatus is immersed in a liquid of R.I , then
i.e wavelength of light decreases. Therefore fringe width
decreases.
(7) Since fringe width is directly proportional to , the fringe produced by the light of shorter wavelength will be narrower compared to these produced by the light of longer wavelength.
(8) If white light is used in place of monochromatic light then there is a central white fringe with a few coloured fringes on both sides.
The path difference to the central fringe is zero for all colours. Consequently, each colour produces a bright fringe here. As they overlap, the white fringe is formed.
In white light, there are a different colour (wavelength). The fringe of one colour is slightly displaced from the fringes of the other colours of the same order . Thus, the fringes of different colours do not exactly overlap. As a result, the edges of the fringes are seen coloured.
Note that, as , therefore,
. In other words, the red fringe will be wider than the violet fringe.
INTERFERENCE IN THIN FILMS
A thin film of liquid (e.g soap film or a layer of oil over water) appears bright and dark when viewed in monochromatic light. This effect is caused due to the interference of light reflected from the top and bottom faces of the film.
From the above fig. light from B and D are interference with each other. The interference is constructive or destructive at a point depending upon path difference of B and D i.e BCD.
Note that when a thin film is viewed in white light (sunlight). It appears coloured. The colour pattern depends upon the thickness of the film, nature of the material of the film and on the position of the observer.
| Introduction | Huygens Principle |
| Refraction and Reflection of Plane waves using Huygens Principle | Coherent and Incoherent Addition of Waves |
| Interference of Light Waves and Young’s Experiment | Diffraction |
| Polarisation | |
IMPORTANT QUESTIONS FOR PRACTICE
1. Two slits are made one millimetre apart and the screen is placed one metre away. What is the fringe separation when blue-green light of wavelength 500 nm is used?
2. What is the effect on the interference fringes in Young’s double-slit experiment due to each of the following operations:
(a) the screen is moved away from the plane of the slits;
(b) the (monochromatic) source is replaced by another
(monochromatic) source of shorter wavelength;
(c) the separation between the two slits is increased;
(d) the source slit is moved closer to the double-slit plane;
(e) the width of the source slit is increased;
(f) the monochromatic source is replaced by a source of white
light?
3. In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.
4. In Young’s double-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ, is K units. What is the intensity of light at a point where path difference is λ/3?
5. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.
(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?
6. In a double-slit experiment, the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take the refractive index of water to be 4/3.
7. In a double-slit experiment using the light of wavelength 600 nm, the angular width of a fringe formed on a distant screen is 0.1º. What is the spacing between the two slits?