Question

Two source S₁ and S₂ of intensity I₁ and I₂ are placed in front of a screen [Figure (a)]. The pattern of intensity distribution seen in the central portion is given by Figure (b).

(a)

(b)

 

1. S₁ and S₂ have the same intensities.
2. S₁ and S₂ have a constant phase difference.
3. S₁ and S₂ have the same phase.
4. S₁ and S₂ have the same wavelength.

विकल्प

• a, b and c

• a, b and d

• b, c and d

• c and d

Answer 1

a, b and d

Explanation:

• For getting the sustained interference the initial phase difference between the interfering waves must remain constant, i.e., sources should be coherent.

For two coherent sources, the resultant intensity is given by `I = I_1 + I_2 + 2sqrt(I_1I_2) cos phi`

• Resultant intensity at the point of observation will be maximum

`I_("max") = I_1 + I_2 + 2sqrt(I_1I_2)`

`I_("max") = (sqrt(I_1) + sqrt(I_2))^2`

• Resultant intensity at the point of observation will be minimum

`I_("min") = I_1 + I_2 - 2sqrt(I_1I_2)`

`I_("min") = (sqrt(I_1) - sqrt(I_2))^2`