Wave Optics Flashcards
(27 cards)
Wavefront is
1) Definition :
2) Perpendicular to :
1) Point vibrating in same phase is called wavefront
2) Perpendicular to direction of propagation of wave or direction of ray
Point source
Spherical wavefront
Linear source
Cylindrical wavefront
Prism
Planar wavefront
Huygen’s principle states that :
Each point of wavefront emerging from the primary wavefront acts as a source of light and other wavelet emerge from it…These wavelet are referred as Secondary wavefront
Tangent to secondary wavelet gives
New position of next wavefront at later time…t
Superposition of Waves
Resultant displacement produced by no. of waves is vector sum of displacement produced by each of the waves
y = y1 + y2 + y3…..
Coherent sources
Sources with :
△ ∅ or ∅ = 0 or constant
Interference
_Superpostion of wave with same frequency & same wavelength
Y1 = A1 sin ( wt - kx )
Y2 = A2 sin ( wt - kx + ∅ )
k = 2π / λ
w = 2 π f
∅ = phase diff / waves
• Interference is just a redistribution of energy
• The total energy remains constant during interference
Resultant amplitude = A = ?
A = √ (A1)² + (A2)² + 2 ( A1 * A2 ) cos ∅
Resultant intensity = I = ?
I = (I 1)² + (I 2)² + 2 √ ( I1 * I2 ) cos ∅
Relation b/w Intensity and Amplitude
I ∝ A²
Phase difference = △∅ = ?
△∅= 2 π * △ x / λ
Or
∅= 2 π * x / λ
{ △x or x = Path difference }
For identical sources :
1) I = ?
2) A = ?
1) I 1 = I 2 = I °
I = 4 I° cos² ( ∅ / 2 )
2) A1 = A2 =A°
A = 2 A° cos ( ∅ / 2 )
Constructive interference
Same amplitude and same direction
Cos ∅ = + 1
∅ = +_ 2n π { n = 0 , 1 , 2 , 3…. }
▪︎ EVEN MULTIPLE OF π
△x = +_ n λ { n = 0 , 1 , 2 , 3…. }
A ( max ) = A1 + A2
I ( max ) = ( √ I 1 + √ I 2 )²
▪︎ Identical sources
A ( max ) = 2 A°
I ( max ) = 4 I°
Destructive interference
Same amplitude & opposite direction
Cos ∅ = - 1
∅ = +_ ( 2n-1 ) π { n = 1 , 2 , 3…. }
▪︎ ODD MULTIPLE OF π
△x = +_ ( n-1) λ /2 { n = 1 , 2 , 3…. }
A ( min ) = A1 - A2
I ( min ) = ( √ I 1 - √ I 2 )²
▪︎ Identical sources
A ( min ) = 0
I ( min ) = 0
Young’s double slit experiment :
1) Path difference
2) Constructive interference
3) Destructive interference
4) Fringe width
5) Angular width
1) △ x = y d / D
2) y = +_ n D λ / d
3) y = +_ ( 2n - 1 ) D λ / 2 d
4) β = D λ / d
5) θ = λ / d
___ Angular width is independent of D
λ = wavelength
D = Screen distance
d = dist b/w slits
YDSE with white light
White light _ all colours
Hence , white light _ △ x = 0 ( doesn’t depend on wavelength for central maxima
YDSE in water :
1) Fringe width in water ?
2) wavelength in water ?
1) β’ ( water ) = β ( air ) / μ
{ β ( air ) = D λ / d }
2) λ’ ( water ) = λ ( air ) / μ
{ β ∝ λ }
Shift in central maxima and entire pattern by same distance cuz of glass slab is__ ?
y = ( μ - 1 ) t D / d
Diffraction
1) Simple definition
2) Fresnal diffraction
3) Frouhofer diffraction
4) Maxima
5) Central maxima
6) Minima
1) Bending of light rays
2) Fresnal diffraction
Screen and source at finite dist
3) Frouhofer diffraction
Screen and source at infinite dist
4) Maxima
θ = +_ n λ / a
β = D λ / a
5) Central maxima
θ = +_ 2 λ / a
β = 2 D λ / a
6) Minima
θ = +_ ( 2n + 1 ) λ / 2a
{ a = slit width )
Fresnal diffraction
1) if D < Z (f)
2) if D > Z (f)
3) Z(f) = ?
1) Particle nature
___ RAY OPTICS DOMINATE
2) Wave nature
___ WAVE OPTICS DOMINATE
3) Z(f) = a² / λ
Resolving power
Ability of an instrument to distinguish b/w two neighboring points
Resolving power ∝ diameter of lens
∝ 1 / Resolving limit
Resolving power
1) Telescope
2) Microscope
1) R.P = 1 / R.L = 2a / 1.22 λ = 1 / θ
2) R.P = 1 / R.L = 2 μ sin θ / 1.22 λ = d
