optics
1
Unit – 4
Engineering Physics
OPTICS
Dr. V.P.N. Padmanaban M.Sc., Ph.D., Associate Professor
1. Interference
Interference of light waves is a superposition phenomenon. This phenomenon was first described by
Thomas Young in 1801. It provided strong evidence for the wave theory of light. In Young’s interference experiment, an incident monochromatic light is diffracted by a slit in the first screen, which then acts as a point source of light that emits semicircular wavefronts. It is then diffracted when passed through two adjacent slits on a second screen, which then acts as two point sources of light. The light waves emerging from these two slits overlap and undergo interference, forming an interference pattern of maxima and minima on the third screen.
2. Theory of Interference Fringes (Analytical Treatment of Interference)
Let S be a monochromatic source of light. S1 and S2 be double slits equidistance from S. Let the distance between S1 and S2 be ‘d’ and ‘D’ be the distance of the screen (AB) from S1 S2 . Let us consider a point P at a distance ‘x’ from the center ‘O’ (Fig.).
2
Condition for bright fringe:
The point P is bright when the path difference is a whole number of multiple of wavelength λ.
That is,
(S2 P - S1 P) = n λ where n = 0, 1, 2, 3,…
From triangle S1QP we have
(1)
(S1P)2 = (S1Q)2 + (QP)2
From the triangle S2RP
(S2P)2 = (S2R)2 + (PR)2
(S2P)2 - (S1P)2 = (S2R)2 + (PR)2 - (S1Q)2 - (QP)2
(S2 P + S1 P) (S2 P - S1 P) = D2 + (x + d / 2)2 - D2 - (x – d / 2)2
2 D (S2 P - S1 P) = (x + d / 2)2 - (x – d / 2)2
We have taken (S2 P + S1 P) = 2 D because the two sources S1 and S2 are close to each other and D is thousand times greater than x or d.
2 D (S2 P - S1 P) = 4 x d / 2
Path difference = (S2 P - S1 P) = xd / D xd/D= nλ
(2)
(3)
x=nλD/d
using eq. (1)
(4)
Equation (4) gives the distance of the bright fringe from the point O. At O, the path difference is zero, hence there is a bright
Unit – 4
Engineering Physics
OPTICS
Dr. V.P.N. Padmanaban M.Sc., Ph.D., Associate Professor
1. Interference
Interference of light waves is a superposition phenomenon. This phenomenon was first described by
Thomas Young in 1801. It provided strong evidence for the wave theory of light. In Young’s interference experiment, an incident monochromatic light is diffracted by a slit in the first screen, which then acts as a point source of light that emits semicircular wavefronts. It is then diffracted when passed through two adjacent slits on a second screen, which then acts as two point sources of light. The light waves emerging from these two slits overlap and undergo interference, forming an interference pattern of maxima and minima on the third screen.
2. Theory of Interference Fringes (Analytical Treatment of Interference)
Let S be a monochromatic source of light. S1 and S2 be double slits equidistance from S. Let the distance between S1 and S2 be ‘d’ and ‘D’ be the distance of the screen (AB) from S1 S2 . Let us consider a point P at a distance ‘x’ from the center ‘O’ (Fig.).
2
Condition for bright fringe:
The point P is bright when the path difference is a whole number of multiple of wavelength λ.
That is,
(S2 P - S1 P) = n λ where n = 0, 1, 2, 3,…
From triangle S1QP we have
(1)
(S1P)2 = (S1Q)2 + (QP)2
From the triangle S2RP
(S2P)2 = (S2R)2 + (PR)2
(S2P)2 - (S1P)2 = (S2R)2 + (PR)2 - (S1Q)2 - (QP)2
(S2 P + S1 P) (S2 P - S1 P) = D2 + (x + d / 2)2 - D2 - (x – d / 2)2
2 D (S2 P - S1 P) = (x + d / 2)2 - (x – d / 2)2
We have taken (S2 P + S1 P) = 2 D because the two sources S1 and S2 are close to each other and D is thousand times greater than x or d.
2 D (S2 P - S1 P) = 4 x d / 2
Path difference = (S2 P - S1 P) = xd / D xd/D= nλ
(2)
(3)
x=nλD/d
using eq. (1)
(4)
Equation (4) gives the distance of the bright fringe from the point O. At O, the path difference is zero, hence there is a bright