Wave Front
Huygen's principle Intensity at any point on screen
Ray Ray i) Each point on a wavefront acts as a fresh Source of new disturbance,
For all maxima I= 4Io
called Secondary waves or wavelets.
Ray
The Secondary wavelets Spread out in all directions with the speed of
spherical Cylindrical
Plane wavefronts
light in the given medium. Note:
wavefronts wavefront
ii) A common envelope or tangent to these Secondary wavelets at any Imax - Imin
later time gives Secondary wavefront at that time Fringe visibility V=
Imax + Imin
Point light source → spherical wavefront
Linear light Source → cylindrical wavefront
Source at infinity → Plane wave front
Resultant Amplitude
YDSE in Liquid
When YDSE setup is immersed in a liqu
Y1= A sin ωt and there is change in wavelength
Incident Reflected
Phase Difference & Path Difference Y2= B sin (ωt + Φ)
wavefront wavefront
n =
c vl l n → refract
= =
Concave Mirror
2π
Δx Resultant R=
v vl ll
Φ= l A2 + B2 + 2AB cosΦ
Spherical cosΦ=1 ⇒ R=Rmax = (A+B)2 = A+B
l or
l µ → ref
Plane Phase Difference & Time Difference lmedium=ll =
n
ll = µ
converging
wavefront 2π cosΦ=-1 ⇒ R=Rmin = (A-B)2 = A-B
wavefront
Φ= T Δt Dl
In air Yn= n
Rmax A+B d
=
Rmin A-B nDll nDl
In medium Yln= =
d dµ
Resultant Intensity
Two independent sources Dl
Convex Mirror Fringe width in air β =
cannot be coherent Intensity ∝ (amplitude)2 d
βair
Dl
Φ In medium βl = ⇒ βmed=
We have, I= I1 + I2 + 2√I1 √I2 cosΦ I= 4Io cos
2
µd µ
2
cosΦ=1 ⇒ I= Imax ⇒ βmed < βair
Plane Spherical
wavefront diverging
wavefront Imax= I1 + I2 + 2√I1 √I2
Imax= (√I1+ √I2)2 Young’s Double-slit experiment (YDSE) Angular fr
ynd l
Incident cosΦ=-1 ⇒ I= Imin Paths difference ΔX = θ=
Refracted d
wavefront wavefront D
Imin= (√I1- √I2)2 ynd
Convex Lens In general ΔX = S1
D
Imax (√I1+ √I2)2 Distance of Minima and Maxima from Central maximum
= S
Imin
(√I1- √I2)2 Maxima Minima
S2
Spherical
nDl Dl
Plane converging Imax ∝ R 2
max
& Imin ∝ R2
min Yn = n = 0,1,2... Yn = (2n-1) n = 1,2...
wavefront wavefront d 2d
Imax R2max (A+B)2
= =
Imin R min2
(A-B)2
Huygen's principle Intensity at any point on screen
Ray Ray i) Each point on a wavefront acts as a fresh Source of new disturbance,
For all maxima I= 4Io
called Secondary waves or wavelets.
Ray
The Secondary wavelets Spread out in all directions with the speed of
spherical Cylindrical
Plane wavefronts
light in the given medium. Note:
wavefronts wavefront
ii) A common envelope or tangent to these Secondary wavelets at any Imax - Imin
later time gives Secondary wavefront at that time Fringe visibility V=
Imax + Imin
Point light source → spherical wavefront
Linear light Source → cylindrical wavefront
Source at infinity → Plane wave front
Resultant Amplitude
YDSE in Liquid
When YDSE setup is immersed in a liqu
Y1= A sin ωt and there is change in wavelength
Incident Reflected
Phase Difference & Path Difference Y2= B sin (ωt + Φ)
wavefront wavefront
n =
c vl l n → refract
= =
Concave Mirror
2π
Δx Resultant R=
v vl ll
Φ= l A2 + B2 + 2AB cosΦ
Spherical cosΦ=1 ⇒ R=Rmax = (A+B)2 = A+B
l or
l µ → ref
Plane Phase Difference & Time Difference lmedium=ll =
n
ll = µ
converging
wavefront 2π cosΦ=-1 ⇒ R=Rmin = (A-B)2 = A-B
wavefront
Φ= T Δt Dl
In air Yn= n
Rmax A+B d
=
Rmin A-B nDll nDl
In medium Yln= =
d dµ
Resultant Intensity
Two independent sources Dl
Convex Mirror Fringe width in air β =
cannot be coherent Intensity ∝ (amplitude)2 d
βair
Dl
Φ In medium βl = ⇒ βmed=
We have, I= I1 + I2 + 2√I1 √I2 cosΦ I= 4Io cos
2
µd µ
2
cosΦ=1 ⇒ I= Imax ⇒ βmed < βair
Plane Spherical
wavefront diverging
wavefront Imax= I1 + I2 + 2√I1 √I2
Imax= (√I1+ √I2)2 Young’s Double-slit experiment (YDSE) Angular fr
ynd l
Incident cosΦ=-1 ⇒ I= Imin Paths difference ΔX = θ=
Refracted d
wavefront wavefront D
Imin= (√I1- √I2)2 ynd
Convex Lens In general ΔX = S1
D
Imax (√I1+ √I2)2 Distance of Minima and Maxima from Central maximum
= S
Imin
(√I1- √I2)2 Maxima Minima
S2
Spherical
nDl Dl
Plane converging Imax ∝ R 2
max
& Imin ∝ R2
min Yn = n = 0,1,2... Yn = (2n-1) n = 1,2...
wavefront wavefront d 2d
Imax R2max (A+B)2
= =
Imin R min2
(A-B)2
