NCERT Physics Class 12 Exemplar Ch 10 Wave Optics Part 4

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Q 21 Four identical monochromatic sources A, B, C, D as shown in the (Fig.) produce waves of the same wavelength and are coherent. Two receiver and 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?

Four identical monochromatic sources A, B, C, D (Q)

Four Identical Monochromatic Sources a, B, C, D (Q)

Four identical monochromatic sources A, B, C, D (Q)

Ans:

Consider the disturbances at which is a distance d from A. Let the wave at because of A be . The path difference of the signal from A with that from B is and hence the phase difference is .

Thus the wave at because of B is

The path difference of the signal from C with that from A is ∴and hence the phase difference is

Thus the wave at because of C is

The path difference between the signal from D with that of A is

Four identical monochromatic sources A, B, C, D (Ans)

Four Identical Monochromatic Sources a, B, C, D (Ans)

Four identical monochromatic sources A, B, C, D (Ans)

If the path difference and hence the phase difference is .

Thus, the signal picked up at is

Let the signal picked up at is from B be

The path difference between signal at D and that at B is 2.

The path difference between signal at A and that at B is

∴∴The phase difference is

Hence,

Similarly.

∴∴Signal picked up by is

Thus picks up the larger signal.

If B is switched off,

picks up t

picks up t

Thus and pick up the same signal.

(iv) Thus a signal at indicates B has been switched off and an enhanced signal at indicates D has been switched off.

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