Question

4) Interference and Diffraction Phenomena (10 points) (a) In a single slit diffraction experiment with a screen far away from the slit, with waves of wavelength 1, there will be no intensity minima if the slit becomes too small compared to the wavelength. What is the minimum slit width (in terms of ) for which no intensity minimum occurs? (Note: if there is no minimum, the screen looks essentially fully illuminated. Think what condition that puts on the angle of any minimum). (b) Why can we readily observe diffraction effects for sound waves and water waves, but not for light? (c) When we have N slits we showed in class that the intensity pattern has sharp narrow peaks, and in between there are multiple minima. Show that for N slits, the minima with zero intensity occur at d sin 0 =mX/N such that the integer m is not a multiple of N. Think about the ph difference required to make all N slits cancel each other (make a sketch if it would help). Show or explain how at the minima, each of the N sources cancels with one or more of the other sources thus yielding a minima.

Answer 1

Sin 8 min ma a sin nin = mi>0 where Du= slit width O in degrees me 1,2,3 --- ls wavelength, Max Slit width occurs sin (90°) = 1 and mal, Then Eqn ① becomes, - atd When the slitwidth is equal to the wavelength of light passing through it, then no diffraction minima are observed.