Q21 of 23 Page 65

Four identical monochromatic sources A, B, C, D as shown in the (Fig.10.7) produce waves of the same wavelength and are coherent. Two receiver R1 and R2 are at great but equal distances from B.


(i) Which of the two receivers picks up the larger signal?


(ii) Which of the two receivers picks up the larger signal when B is turned off?


(iii) Which of the two receivers picks up the larger signal when D is turned off?


(iv) Which of the two receivers can distinguish which of the sources B or D has been turned off?


(i) Let the wave at R1 because of A be,


The path difference of B with A is λ /2, i.e. phase difference is π


∴, the wave at B because of R1 is


The path difference of C with A is λ i.e. phase difference is 2π


∴, the wave at B because of R1 is


The path difference of D with A is






∴ the phase difference here is π


The wave D can be represented as



∴ the signal at R1 due to all sources Y1=A+B+C+D



Let the signal received by R2 because of B be



The path difference of D with B is λ/2


∴ i.e. phase difference is π


∴, the wave at D because of R2 is


The path difference of A with B is






∴ the phase difference here is 0


The wave A can be represented as



Similarly wave C can be represented as



∴ the signal at R2 due to all sources Y2=a+b+c+d





∴ R1 picks up larger signal


(ii) If B is switched off,






Thus R1 and R2 picks same signal


(iii) If D is switched off,






Thus R2 picks larger signal


(iv) A signal at R1 indicates B has been switched off and an


enhanced signal at R2 indicates D has been switched off


More from this chapter

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19

Figure 10.5 shown a two-slit arrangement with a source which emits unpolarised light. P is a polarizer with axis whose direction is not given. If I0 is the intensity of the principal maxima when no polarizer is present, calculate in the present case, the intensity of the principal maxima as well as of the first minima.


 20

A small transparent slab containing material of μ =1.5 is placed along AS2 (Fig.10.6). What will be the distance from O of the principal maxima and of the first minima on either side of the principal maxima obtained in the absence of the glass slab.


AC = CO = D, S1C = S2C = d << D


 22

The optical properties of a medium are governed by the relative permittivity (εr) and relative permeability (μr ). The refractive index is defined as For ordinary material εr > 0 and μr > 0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with εr < 0 and μr < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials As light enters a medium of such refractive index the phases travel away from the direction of propagation.

(i) According to the description above show that if rays of light enter such a medium from air (refractive index = 1) at an angle in 2nd quadrant, them the refracted beam is in the 3rd quadrant.


(ii) Prove that Snell’s law holds for such a medium.


 23

To ensure almost 100 per cent transitivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF2 (n = 1.38). What should the thickness of the film be so that at the center of the visible spectrum (5500 Å) there is maximum transmission.