Question
Coherent(laser)light of wavelength 550 x 10-9m is incident on two slits 0.008 mm apart. These slits become coherent, in-phase sources of cylindrical wave fronts which interfere and produce maxima and minima in intensity,"bright lines", on a screen 70 cm away. Draw and lable figure with symbols L1,L2,R,,d,D and y.
a)Calculate the first three "+y" positions on the screen for intensity maxima relative to the central maximum. Here it is appropriate to use the small angle approximation.
b)At a position y = 3.2 cm on the xcreen, what is the phase difference between the two incident waves?
Explanation / Answer
Given Wavelength of incident light = 550*10-9 m Seperation between two slits d = 0.008 mm = ( 0.008 mm ) ( 0.001 / 1 mm ) = 8*10-6 m Distance slits and screen L = 70 cm = ( 70 cm ) ( 0.01 m / 1 cm ) = 0.7 m a) Linear positin of bright fringe from central maximum at small angles y = L ( m / d ) For m =1 y = L / d = ( 0.7 m ) ( 550*10-9 m ) / ( 8*10-6 m ) = 0.048 m For m =2 y = 2L / d = 2 ( 0.07 m ) ( 550*10-9 m ) / ( 8*10-6 m ) = 0.096 m For m =3 y = 3L / d = 3( 0.07 m ) ( 550*10-9 m ) / ( 8*10-6 m ) = 0.148 m = 2 ( 0.07 m ) ( 550*10-9 m ) / ( 8*10-6 m ) = 0.096 m For m =3 y = 3L / d = 3( 0.07 m ) ( 550*10-9 m ) / ( 8*10-6 m ) = 0.148 m = 3( 0.07 m ) ( 550*10-9 m ) / ( 8*10-6 m ) = 0.148 m __________________________________________________ b)At a position y = 3.2 cm = ( 3.2 cm ) ( 0.01 m / 1 cm ) = 0.032 m y = L tan tan = y / L = 0.032 m / 0.7 m = 2.617 o Path difference d sin = ( 8*10-6 m ) sin 2.617 = 3.65*10-7 m Phase difference = ( 2 / ) d sin = 2 ( 3.65*10-7 m ) / ( 550*10-9 m ) = 1.32 = 4.169 o