Wave Optics Revision Notes - IIT JEE/NEET Preparation | Nucleon

## Wave Optics

• PRINCIPLE OF SUPERPOSITION
• When two or more waves simultaneously pass through a point, the disturbance of the point is given by the
sum of the disturbances each wave would produce in absence of the other wave(s). In case of wave on
string disturbance means displacement, in case of sound wave it means pressure change, in case of
Electromagnetic Waves. it is electric field or magnetic field. Superposition of two light travelling in almost
same direction results in modification in the distribution of intensity of light in the region of superposition.
This phenomenon is called interference.

• WAVEFRONTS
• Consider a wave spreading out on the surface of water after a stone is thrown in. Every point on the surface
oscillates. At any time, a photograph of the surface would show circular rings on which the disturbance is
maximum. Clearly, all points on such a circle are oscillating in phase because they are at the same distance
from the source. Such a locus of points which oscillate in phase is an example of a wavefront

• COHERENCE
• Two sources which vibrate with a fixed phase difference between them are said to be
coherent. The phase differences between light coming form such sources does not
depend on time.

• YOUNG’S DOUBLE SLIT EXPERIMENT (Y.D.S.E.)
• In 1802 Thomas Young devised a method to produce a stationary interference pattern. This was based upon
division of a single wavefront into two; these two wavefronts acted as if they emanated from two sources having
a fixed phase relationship. Hence when they were allowed to interfere, stationary interference pattern was observed

• Analysis of Interference Pattern
• We have insured in the above arrangement that the light wave
passing through S1 is in phase with that passing through S

• Fringe width
• It is the distance between two maxima of successive order on one side of the central maxima. This is
also equal to distance between two successive minima

• Maximum order of Interference Fringes
• Maximum order of Interference Fringes

• Intensity
• Suppose the electric field components of the light waves arriving at point P(in the Figure : 3)
from the two slits S1 and S2 vary with time as

• SHAPE OF INTERFERENCE FRINGES IN YDSE
• We discuss the shape of fringes when two pinholes are used instead of the two slits in YDSE.
Fringes are locus of points which move in such a way that its path difference from the two slits remains constant

• GEOMETRICAL PATH & OPTICAL PATH
• GEOMETRICAL PATH & OPTICAL PATH

• YDSE WITH OBLIQUE INCIDENCE
• YDSE WITH OBLIQUE INCIDENCE

• THIN-FILM INTERFERENCE
• In YDSE we obtained two coherent source from a single
(incoherent) source by division of wave-front. Here we do
the same by division of Amplitude (into reflected and refracted
wave).

• HUYGENS CONSTRUCTION
• Huygens, the Dutch physicist and astronomer of the seventeenth century, gave a beautiful
geometrical description of wave propagation. We can guess that he must have
seen water waves many times in the canals of his native place Holland. A stick placed
in water and oscillated up and down becomes a source of waves. Since the surface of
water is two dimensional, the resulting wavefronts would be circles instead of spheres

• REFLECTION AND REFRACTION
• We can use a modified form of Huygens' construction to understand reflection and refraction of light. Figure
(10.2a) shows an incident wavefront which makes an angle ‘i’ with the surface separating two media, for example,
air and water. The phase speeds in the two media are v1 and v2. We can see that when the point A on the
incident wavefront strikes the surface, the point B still has to travel a distance BC = AC sin i, and this takes a
time t = BC/v1 = AC (sin i) / v1. After a time t, a secondary wavefront of radius v2t with A as centre would have
travelled into medium 2. The secondary wavefront with C as centre would have just started, i.e.. would have zero
radius. We also show a secondary wavelet originating from a point D in between A and C. Its radius is less than
v2t. The wavefront in medium 2 is thus a line passing through C and tangent to the circle centred on A. We can

• REFLECTION AND REFRACTION
• where n2 is the refractive index of medium 2 with respect to vacuum, also called the absolute refractive index of
the medium. A similar equation defines absolute refractive index n1 of the first medium. From Eq. we then get n21

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