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**The periodic waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is: **

### Options

(a) I₁ + I₂

(b) (√I₁ + √I₂)²

(c) (√I₁ – √I₂)²

(d) 2 (I₁ + I₂)

### Correct Answer:

2 (I₁ + I₂)

### Explanation:

The resultant intensity of two periodic waves at a point is given by

I = I₁ + I₂ + 2 √I₁I₂ . cos ?.

Resultant intensity is max. if cos ? = -1

i.e Iₘₐₓ = I₁ + I₂ + 2 √I₁I₂

Resultant intensity is min. if cos ? = +1

i.e, Iₘᵢₙ = I₁ + I₂ – 2 √I₁I₂

Therefore, the sum of the max. and min. intensities is Iₘₐₓ + Iₘᵢₙ

= I₁ + I₂ + 2 √I₁I₂ + I₁ + I₂ – 2 √I₁I₂

= 2 (I₁ + I₂)

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Topics: Ray Optics
(94)

Subject: Physics
(2479)

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