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Thursday, 9 March 2017

Wave Optics - III


Young’s Experiment
Two parallel and very close slits S1and S2 (illuminated by another narrow slit) behave like two coherent sources and produce on a screen a pattern of dark and bright bands – interference fringes.
For a point P on the screen, the path difference
Where d is the separation between two slits, D1 is the distance between the slits and the screen and y1 is the distance of the point of P from the central fringe.
For constructive interference (bright band), the path difference must be an integer multiple of l , i.e.,

The separation Δy1between adjacent bright (or dark) fringes is,
using which l can be measured.

Young’s Double Slit Interference Experiment:

where D is the distance between the slits & the screen d is the distance between the two slits

Constructive Interference:
a) Phase difference : D f = 2p n  where n is an integer

b) Path difference: DX = nl  where n is an integer

Destructive interference:

Diffraction due to Single Slit:


Where D is the distance of the slit from the screen d is the slit width

Condition for the Minima on the either side of the Central Maxima: 


Relation between phase difference & path difference:
Where f is the phase difference & X is the path difference

Diffraction:
a) It refers to light spreading out from narrow holes and slits, and bending around corners and obstacles.

b) The single-slit diffraction pattern shows the central maximum ( atq  = 0) , zero
intensity at angular separation

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