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Principle of Superposition

1- two monoch...

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1- two monochromatic waves producing from two coherent sources have the displacement represented by y1=acoswt and y2=acos(wt+fi) where fi is phase difference .show that resultants intensity at a point of superpositions is given by I=4icos^2fi/2.
w=omega .

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Q. (a) Consider two coherent sources

S_{1}

S_{2}

producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by

S_{1}

Y_{1} = a c o s ω t

and the displacement by

S_{2}

Y_{2} = a c o s (ω t + ϕ)

. Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be

I = 4 a^{2} c o s^{2} \frac{ϕ}{2}

. Hence, establish the conditions for constructive and destructive interference.
(b) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slits is increased; (ii) the monochromatic source is replaced by a source of white light.

Q. (a) (i)'Two independent monochromatic sources of light cannot produce a sustained interference pattern'. Give reason.
(ii) Light wave each of amplitude "a" and frequency "

ω

", emanating from two coherent light sources superpose at a point. If the displacements due to these waves is given by

y_{1} = a c o s ω t

y_{2} = a c o s (ω t + ϕ)

ϕ

is the phase difference between the two, obtain the expression for the resultant intensity at the point.
(b) 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. Find out the intensity of light at a point where path difference is

λ / 3

Q. Light waves from two coherent sources having intensities

I

2 I

cross each other at a point with a phase difference of

60^{o}

. What is the resultant intensity at the point?

Q. Two coherent waves are represented by

Y_{1} = A_{1} cos ω t

Y_{2} = A_{2} sin ω t

.
The resultant intensity due to interference is proportional to

Q. Waves from coherent sources, having intensity

I_{0}

each, meets at point

P

. What is the resultant intensity of two waves at

P

, if the path difference between the waves is

\frac{λ}{3}

?

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