Interference of light waves

Interference of light refers to the redistribution of light energy due to superposition of two light waves. This superposition leads to a pattern of alternate dark and bright fringes. These dark and bright fringes are called as minima and maxima respectively.

1. Interference of light 1

2. What is Light? Light is an electromagnetic radiation refers to visible regions of electromagnetic spectrum corresponding to the wavelength range of 400nm to 760nm which has transverse vibrations. Wave

3. General Definitions The Wavelength of a sin wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, as shown. The frequency, f, of a wave is the number of waves passing a point in a certain time. We normally use a time of one second, so this gives frequency the unit hertz (Hz), since one hertz is equal to one wave per second.

4. Principle of Superposition “ Whenever two or more waves superimpose in a medium, the total displacement at any point is equal to the vector sum of individual displacement of waves at that point” If Y 1 , Y 2 , Y 3 …are different displacement vector due to the waves 1,2,3 …acting separately then according to the principle of superposition the resultant displacement is given by Y=Y 1 +Y 2 +Y 3 +……

5. INT E RFERENCE is the process in which two or more waves of the same frequency - be it light, sound, or other electromagnetic waves - either reinforce or cancel each other, the amplitude of the resulting wave being equal to the sum of the amplitudes of the combining waves. For example, if at a given instant in time and location along the medium, the crest of one wave meets the crest of a second wave, they will interfere in such a manner as to produce a "super-crest." Similarly, the interference of a trough and a trough interfere constructively to produce a "super-trough." This is called constructive interference. If the two amplitudes have opposite signs, they will subtract to form a combined wave with a lower amplitude. For example, the interaction of a crest with a trough is an example of destructive interference. Destructive interference has the tendency to decrease the resulting amount of displacement of the medium. The bright bands show constructive interference of light. The dark bands show destructive interference of light.

6. Nature of Interference depends on the path difference or phase difference between the interfering waves. 8 constructive interference. Path difference is integral multiple of wavelength δ = nλ (Phase difference φ= 2nπ)

7. Nature of Interference depends on the path difference or phase difference between the interfering waves. 9 destructive interference. Path difference is Odd integral multiple of half of the wavelength δ = (2n+1)λ/2 (Phase difference φ= (2n+1)π)

8. Conditions for SUSTAINED interference pattern. Interfering light waves should be of same frequency. The two sources must be coherent. Interfering light waves should travel almost in the same direction. Interfering light waves should be of almost same amplitude. The two sources producing the coherent light must be narrow . 10

9. YOUNG’S DOUBLE SLIT EXPERIMENT Each slit acts as an independent source of waves. 6 Waves from each slit interfere c o nst r uct iv e l y or destructively at the screen producing dark or bright bands

10. YOUNG’S DOUBLE SLIT EXPERIMENT: Theory 12

11. YOUNG’S DOUBLE SLIT EXPERIMENT: Theory For P to be a bright point constructive interference should take place. d sin θ= n λ. since sin θ= x/D xd/D= n λ or x= n λD/d 13 the next bright point is x′= (n+1) λD/d distance between two successive bright spots( fringes) is x′ – x=β width between two successive bright fringes is β= λD/d

12. YOUNG’S DOUBLE SLIT EXPERIMENT: Theory For P to be a dark point destructive interference should take place. d sin θ= (2n+1) λ/2. since sin θ= x/D xd/D= (n+1/2) λ or x= (n+1/2) λD/d next dark point is x′= (n+1+1/2) λD/d distance between two successive bright spots( fringes) is x′ – x=β 14 width between two successive dark fringes is β= λD/d

13. : . Coherent sources 15 If two light sources emitting light waves with the same phase or having a constant phase difference are called coherent sources . Two light sources are said to be coherent if they emit light waves of the same frequency with same phase or a constant phase difference.

14. : . Coherent sources Two independent sources cannot emit light with constant phase difference as their emission is extremely random. Thus they can not be coherent sources NOTE : coherent sources from a single source are obtained in two distinct ways . 16

15. : . 1. Coherent sources by division of wavefront: In this method wavefront of a light source is divided into two or more parts through refraction. Light passing through a biprism can produce two virtual images. The two virtual images act as coherent sources . Example : 17

16. 1. Coherent sources by division of wavefront: Light coming from S 1 and S 2 are coherent 18

17. 2. Coherent sources by division of amplitude 19 In this method wavefront of a light source is subjected to partial reflection and partial refraction. : Light reflected by a thin film or refracted through a transparent thin film. We have here two sets of wavefronts moving in the same direction travelling in phase. Example :

18. 2. Coherent sources by division of amplitude Reflected waves are coherent Refracted waves are coherent 20