Question

Two identical light waves having phase difference 'Φ' propagate in same direction. When they superpose, the intensity of the resultant wave is proportional to ______.

Options

• cos² Φ

• cos² `Φ/2`

• cos² `Φ/3`

• cos² `Φ/4`

Answer 1

Two identical light waves having phase difference 'Φ' propagate in same direction. When they superpose, the intensity of the resultant wave is proportional to cos² `underlinebb(Φ/2)`.

Explanation:

A² = a₁² + a₂² + 2a₁a₂ cos Φ, where A is the amplitude of the resultant wave and given that, a₁ = a₂ = a,

where a is the amplitude of the individual waves.

∴ A² = 2a²(1 + cos Φ) = 2a²(1 + 2cos²  `Φ/2` - 1) ⇒ A² α cos² `Φ/2`

Now, I α A²

∴ I α A² α cos² `Φ/2` ⇒ α cos² `Φ/2`