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Interference of light waves- 1, Interference of light waves- 2 is considered one of the most asked concept.
29 Questions around this concept.
Two waves and superimpose to form a resultant wave. The amplitude of this resultant wave is given by
The time of exposure for a photographic print is 10 seconds when a lamp of 50 cd is placed at 1 m from it. Then another lamp of luminous intensity I is used and is kept at 2 m from it. If the time of exposure now is 20 s, the value of I (in cd) is
A parallel beam of white light falls on a thin film whose refractive index is 1.33. If the angle of incidence is , then the thickness of the film for the reflected light to be coloured yellow most intensively must be
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The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio will be :
In the Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is is K, ( being the wave length of light used). The intensity at a point where the path difference is , will be:
In Young's double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double of that from the other slit. If Im be the maximum intensity, the resultant intensity I when they interfere at phase difference is given by :
Two beams of light having intensities I and 4 I interfere to produce a fringe pattern on the screen. The phase difference between the beams is at point a and at point B. The difference of intensities at A and B is
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The intensity of the central bright fringe due to interference of two identical coherent monochromatic sources is I. If one of the sources is switched off, then the intensity of the central bright fringe becomes
In an interference pattern by two identical slits, the intensity of central maxima is . If one slit is closed, the intensity of central maxima changes to . Then and are related by
Interference fringes from sodium light in a double slit experiment have an angular width , To increase the fringe width by , the new wavelength should be
In order to observe interference in light waves, the following conditions must be met:
Coherent sources-
Two sources are said to be coherent if they produce waves of the same frequency with a constant phase difference.
Phase difference :
The difference between the phases of two waves at a point is called phase difference.
Path difference :
The difference in path lengths of two waves meeting at a point is called path difference between the waves at that point.
And The relation between Phase difference and Path difference is given as
where
Principle of Super Position-
According to the principle of Super Position of waves, when two or more waves meet at a point, then the resultant wave has a displacement (y) which is the algebraic sum of the displacements ( ) of each wave.
i.e
consider two waves with the equations as
where is the phase difference between waves .
And According to the principle of Super Position of waves
Now let
Putting this in equation (1) we get
thus we get the equation of the resultant wave as
where A=Resultant amplitude of two waves
and
and
where
the amplitude of wave 1
the amplitude of wave 2
Resultant Intensity of two waves (I)-
Using
we get
where
The intensity of wave 1
The intensity of wave 2
or
Interference of Light-
It is of the following two types.
1. Constructive interference-
i.e we will see bright fringe/spot.
The phase difference between the waves at the point of observation is
Path difference between the waves at the point of observation is
The resultant amplitude at the point of observation will be maximum
Resultant intensity at the point of observation will be maximum
2. Destructive interference-
i.e we will see dark fringe/spot.
The phase difference between the waves at the point of observation is
Path difference between the waves at the point of observation is
The resultant amplitude at the point of observation will be maximum
Resultant intensity at the point of observation will be maximum
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