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In the double-slit experiment of the figure below, the viewing screen is at dist

ID: 1697739 • Letter: I

Question

In the double-slit experiment of the figure below, the viewing screen is at distance D = 4.00 m, point P lies at distance y = 13.0 cm from the center of the pattern, the slit separation d is 4.50 µm, and the wavelength is 650 nm. The angle serves as a convenient locator for P. For D >> d, we can approximate rays r1 and r2 as being parallel, at angle to the central axis.

(a) Determine where point P is in the interference pattern by giving the phase difference at point P in radians.
1

(b) What is the ratio of the intensity at point P to the intensity at the center of the pattern (IP / Icenter)?
2

Explanation / Answer

The wave length of light = 650nm

the seperation between slits d = 4.50m

the distance between screen D = 4.0m

the postion of point P is y = 13cm

(a) The position of P in terms of phase difference

           = 2/ dsin

              =[ 2/(650*10^-9)](4.5*10^-6)(y/D)

since for small angles sin tan = y/D

            = 0.0435*10^3 (13*10^-2/4)

            = 0.45 rad = 1.413 rad

(b) The ratio of intensity

           I/I0 = 4cos^2(/2)

                  = 4cos^2(1.413/2)

                   =2.3