# Physics Assignment Help With Young's Double-slit Experiment

## 14.12 Young's Double-slit Experiment

### 14.12.1 Analytical treatment of Young's Double slit experiment

To analyze the interference pattern and investigate the spacing of the interference fringes, consider the geometry in figure. Let *S* be a narrow slit illuminated by monochromatic light, and *S*1 and *S*2 two parallel narrow slits very close to each other and equidistant from *S*. The light from *S* arrives at *S*1 and *S*2 in the same phase. Beyond *S*1 and *S*2 the waves proceed as if they started from *S*1 and *S*2 with the same phase because the two slits are equidistant from S.

To find the intensity at a point *P* on the screen, we join *S*1*P* and *S*2*P*. The two waves arrive at P from *S*1 and *S*2 having traversed different paths *S*1*P* and *S*2*P*. Let us calculate this path difference *S*2*P* – *S*1*P*. Let,

*y* = distance of P from *P*0, the central point on the screen

*d* = separation of two slits *S*1 and *S*.

D= distance between slits and screen

*S*2*A* = *d* sin q¢ = *d* sin q = *d* tan q,

as for small q, sin q = tan q. As can be seen from the figure, tan q = *y*/D.

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Now the intensity at the point *P* is a maximum or minimum according as the path difference

Hence, for bright fringes (maxima).

(bright fringes)

The number *n* is called the order of the fringe. Thus the fringes with *n* = 0, 1, 2, …. etc. are called zero, first, second…..etc. orders. The zeroth order fringe corresponds to the central maximum, the first order fringe corresponds to the first bright fringe on either side of the central maximum, and so on.

For dark fringes (minima),

where *n*= ± 1, ± 2, ± 3 ….

(Dark fringes)

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