Q20 of 23 Page 65

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


Whenever a transparent slab of refractive index μ and thickness t is inserted in the path of the ray the fringes on the screen shifts by (μ-1) t towards the slab.

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


L=d/4, μ=1.5


∴ the optical path difference is given by



For principal maxima OPD=0, i.e.





The distance from O to principal maxima is,



The path difference for first minima is ± (λ/2)


i.e.




Since diffraction occurs when slit width is equals to the wavelength i.e. λ =d




Considering the positive side,



Considering the negative side,



The distance of first principal minima from O on the positive side is,



The distance of first principal minima from O on the negative side is,



More from this chapter

All 23 →
18

Consider a two slit interference arrangements (Fig. 10.4) such that the distance of the screen from the slits is half the distance between the slits. Obtain the value of D in terms of such that the first minima on the screen falls at a distance D from the centre O.


 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.


 21

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?


 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.