Question

A point is situated at 6.5 cm and 6.65 cm from two coherent sources. Find the nature of illumination at the point, if wavelength of light is 5000 Å.

Answer 1

Given: 

x₁ = 6.5 cm = 6.5 x 10^-2 m,

x₂ = 6.65 cm = 6.65 x 10^-2 m,

λ = 5000 Å = 5 x 10^-7 m

To find : Nature of illumination at the point

Formula: Δ x = n λ

Calculation: Path difference is given by,

Δ x = x_{2 -} x₁ = 6.665 x 10^-2 - 6.5 x 10^-2 = 0.15 x 10^-2 m

From formula,

n = \(\frac{Δx}{λ}\)

n = \(\frac{0.15\times10^{-2}}{5\times10^{-7}}\)

= 3000

∴ Δ x = 3000λ = 6000\(\frac{λ}{2}\)

As the path difference is even multiple of \(\frac{λ}{2}\) , the point is bright. 

Ans: The point is bright.