PHYSICS

WAVES

WAVE OPTICS_INTERFERENCE

MATHEMATICS

MISCELLANEOUS

PHYSICS

WAVES

WAVE_OPTICS_INTERFERENCCE



interf

Resultant amplitude

|a₁ + a₂| = √(a₁² + a₂² + 2a₁a₂*cosϕ)

Resultant intensity

I = I₁ + I₂ + 2√(I₁I₂)*cosϕ

Phase difference - Path difference relationship


path difference = (λ/2π) * (phase difference)

Amlitude-intensity relationship


I = ka²

MAX intensity

Imax = (√I₁ + √I₂)²

MIN intensity

Imin = (√I₁ - √I₂)²

MAX amplitude

amax = a₁ + a₂
↑condition for constructive interference
from cosϕ = 1
⇒ ϕ = 0
or
ϕ = 2nπ n = 0, 1, 2, ...
So, CONSTRUCTIVE INTERFERENCE
HAPPENS WHEN PHASE DIFFERENCE
Is a multiple of 2π.

⇒ From Δx = (λ/2π)ϕ,
Δx = (λ/2π)*(2nπ) (∵ϕ = 2nπ)
= nλ
So, Δx = nλ ▄

MIN amplitude

amin = a₁ - a₂
↑condition for destructive interference
for minimum |a₁⃗ + a₂⃗|,
cosϕ = -1 ⇒ ϕ = (2n-1)π
So, DESTRUCTIVE INTERFERENCE
HAPPENS WHEN PHASE DIFFERENCE
Is an odd multiple of π.

⇒ From Δx = (λ/2π)*(2n - 1)π,

SO, Δx = (2n - 1)(λ/2) ▄

MATHEMATICS

Miscellaneous