Wave Optics Flashcards
Intensity and amplitude relation
I ∝ A²
Amplitude of resultant wave
A =√ (A₁² + A₂² + 2A₁A₂cosΦ)
Resultant intensity
I = I₁ + I₂ +2 √ (I₁I₂cosΦ)
Intensity max and min
- Iₘₐₓ = ( √I₁ + √I₂ )²
= (A₁ + A₂)² - Iₘᵢₙ = ( √I₁ - √I₂ )²
= (A₁ - A₂)²
Intensity at given point
I = Iₘₐₓcos²(Φ/2)
Iₘₐₓ = 4Io
For constructive interference
- phase diff, Φ = 2nπ
- path diff, ∆x = nλ
n=0,1,2,3…
For destructive interference
- phase diff, Φ = (2n-1)π
- path diff, ∆x = (2n-1)λ/2
n=1,2,3…
Path difference
- ∆x = dsinθ
- ∆x = dy/D
Fringe width β
β = Dλ/d
Angular fringe width
θ = β/D
θ will be in radians
For diffraction
Position of secondary minimum
asinθ = nλ
(n=1,2,3…)
Diffraction can be observed in
Both sound and light waves
For diffraction
Position of secondary maximum
asinθ = (2n +1)λ/2
(n=1,2,3…)
Fringe width in medium of refractive index n
β’ = Dλ/nd
β’ = β/n
β’: fringe width in medium
β: fringe width in air
When a wave travels from air into glass, what will not change?
Frequency
For a line source intensity varies with distance r as
1/r
Distance of nth bright from central maxima
y = nDλ/d
(n=0,1,2,3…)
Distance of nth dark from central maxima
y = (2n -1)Dλ/2d
(n=1,2,3…)
Brewsters law
n = tanθ
θ is angle of polarisation
n is refractive index of medium
Malu’s law
I₂ = I₁cos²θ
- I₁ = I₀/2
- for crossed polaroids θ=0, ie, I₂ =0
In diffraction
Angular width of central maximum
2λ/a
In diffraction
Linear width of central maximum
- 2Dλ/a
- for lens of focal length f: 2fλ/a
