(a)  In young’s double slit experiment, deduce the conditions for obtaining constructive and destructive interference fringes. Hence, deduce the expression for the fringe width.

(b)  Show that the fringe pattern on the screen is actually a superposition of slit diffraction from each slit.

(c)   What should be the width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern, for green light of wavelength 500 nm, if the separation between two slits is 1 mm?

Asked by Topperlearning User | 10th Jul, 2015, 12:47: PM

Expert Answer:

(a)  Young’s double slit experiment demonstrated the phenomenon of interference of light. Consider two fine slits S1 and S2 at a small distance d apart. Let the slits be illuminated by a monochromatic source of light of wavelength l. Let GG′ be a screen kept at a distance D from the slits. The two waves emanating from slits S1 and S2 superimpose on each other resulting in the formation of an interference pattern on the screen placed parallel to the slits.

Let O be the centre of the distance between the slits. The intensity of light at a point on the screen will depend on the path difference between the two waves reaching that point.  Consider an arbitrary point P at a distance x from O on the screen. 

Path difference between two waves at P = S2P − S1P

 

(a)  The intensity variation in the fringe pattern obtained on a screen in a Young’s double slit experiment corresponds to both single slit diffraction and double slit interference because the two sources are slits of finite width in the double slit experiment.

 

If a lens is placed in front of the double slits and when one of the slit S1 is closed and the other kept open, a single slit diffraction is formed on the screen. A similar diffraction pattern is obtained on the screen if the slit S1 is kept open and S2 is closed. Both diffraction patterns form on the same position on the screen in the focal plane of the lens. When both slits open simultaneously, the resulting total intensity pattern on the screen is actually the superposition of the single slit diffraction pattern formed by waves from various point sources of each slit and a double slit interference pattern as shown. The actual double slit intensity pattern consists of the interference pattern (solid lines) formed within the diffraction pattern (dotted lines).



Answered by  | 10th Jul, 2015, 02:47: PM