Question

Two identical coherent sources are placed on a diameter of a circle of radius R at separation x (<< R) symmetrical about the centre of the circle. The sources emit identical wavelength λ each. The number of points on the circle of maximum intensity is (x = 5λ).  

Solution

Correct option is

20

 

Path difference at P is

                

For intensity to be maximum,

                

     

  

  

Substituting x = 5λ, we get

               

Therefore, in all four quadrants there can be 20 maxima. There are more maxima at θ = 0o and θ = 180o. But n = 5 corresponds to θ = 90o and θ = 270o which are coming only twice while we have multiplied if four times. Therefore, total number of maxima are still 20, i.e., n = 1 to 4 in four quadrants (total 16) plus more at θ = 0o, 90o, 180o and 270o.

SIMILAR QUESTIONS

Q1

Microwave from a transmitter are directed normally towards a plane reflector. A detector. A detector moves along the normal to the reflector. Between positions of 14 successive maxima the detector travels a distance 0.14 m. The frequency of the transmitter is (c = 3 × 108 m/s)    

Q2

In a Young’s double-slit experiment, the separation between the slits is d, distance between the slit and screen is D(D >> d). In the interference pattern, there is a maxima exactly in front of each slit. Then, the possible wavelength(s) used in the experiment are  

Q3

In a double-slit experiment, two parallel slits are illuminated first by light of wavelength 400 nm and then by light of unknown wavelength. The fourth-order dark fringe resulting from the known wavelength of light falls in the same place on the screen as the second-order bright fringe from the unknown wavelength. The value of unknown wavelength of the light is 

Q4

Light is incident at an angle Ï• with the normal to a plane containing two slits of separation d. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle Ï• and outgoing angle θ.

                                                                     

Q5

In Young’s double-slit experiment, the slits are illuminated by monochromatic light. The entire set-up is immersed in pure water. Which of the following act cannot restore the original fringe width?

Q6

Blue light of wavelength 480 nm is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incident. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6, what is the minimum thickness of the oil film (other than zero)?

Q7

The slits in a double-slit interference experiment are illuminated by orange light (λ = 60 nm). A thin transparent plastic of thickness t is placed in front of one of the slits. The number of fringes shifting on screen is plotted versus the refractive index μ of the plastic in graph shown in fig. The value of t is

                                                  

Q8

In a YDSE with identical slits, the intensity of the central bright fringe is . If one of the slits is covered, the intensity at the same point is

Q9

The maximum intensity in Young’s double-slit experiment is I0. Distance between the slits is d = 5λ, where λ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance D = d?       

Q10

In Young’s double-slit experiment  (d = distance between slits, D = distance of screen from the slits). At a point P on the screen, resulting intensity is equal to the intensity due to the individual slitI0. Then, the distance of point P from the central maximum is (λ = 6000 Ã…)