Q27 of 79 Page 380

Two coherent point sources S1 and S2 vibrating in phase emit light of wavelength λ. The separation between the sources is 2λ. Consider a line passing through S2 and perpendicular to the line S1S2. What is the smallest distance from S2 where a minimum of intensity occurs?

The following diagram describes the situation.


Here, forms a right angled triangle.


The path difference is {from Pythagoras theorem}


To have a minimum at O, the path difference should be .


Therefore,



Squaring both sides,





Now, for n=0,



for n=1,



for n=2,



As negative values are not allowed, the minimum values is .


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25

White coherent light (400 nm—700 nm) is sent through the slits of a Young’s double slit experiment (figure 17-E3). The separation between the slits is 0.5 mm and the screen is 50 cm away from the slits. There is a hole in the screen at a point 1.0 mm away (along the width of the fringes) from the central line. (a) Which wavelength(s) will be absent in the light coming from the hole? (b) which wavelength(s) will have a strong intensity?


 26

Consider the arrangement shown in figure (17-E4). The distance D is large compared to the separation d between the slits. (a) Find the minimum value of d so that there is a dark fringe at O. (b) Suppose d has this value. Find the distance x at which the next bright fringe is formed. (e) Find the fringe-width.


 28

Figure (17-E5) shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let BP0 - AP0 = λ/3 and D >> λ. (a) Show that in this case . (b) Show that the intensity at P0 is three times the intensity due to any of the three slits individually.


 29

In a Young’s double slit experiment, the separation between the slits = 2.0 mm, the wavelength of the light = 600 am and the distance of the screen from the slits = 2.0 m. If the intensity at the center of the central maximum is 0.20 W m-2, what will be the intensity at a point 0.5 cm away from this center along the width of the fringes?