diffraction at a single slit
DESCRIPTION
Diffraction at a single slit. a = 4 λ. a = λ. a = 2 λ. Semi circular wave fronts. First minima & maxima become visible. Diffraction is the spreading of wavefronts around corners and obstacles. If the slit gets narrower diffraction increases. - PowerPoint PPT PresentationTRANSCRIPT
Diffraction at a single slit
a = λSemi circular wave fronts
a = 2 λFirst minima & maxima
become visible
a = 4 λ
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Diffraction at a single slit
a = λSemi circular wave fronts
a = 2 λFirst minima & maxima
become visible
a = 4 λ
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Diffraction at a single slit
a = λSemi circular wave fronts
a = 2 λFirst minima & maxima
become visible
a = 4 λ
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Diffraction at a single slit
a = λSemi circular wave fronts
a = 2 λFirst minima & maxima
become visible
a = 4 λ
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Diffraction at a single slit
a = λSemi circular wave fronts
a = 2 λFirst minima & maxima
become visible
a = 4 λ
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Diffraction at a single slit
a = λSemi circular wave fronts
a = 2 λFirst minima & maxima
become visible
a = 4 λ
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
It can be shown that the first minima occurs when sin Ə = λ/a .
aT
First minima
Central maximaƏ
It can be shown that the first minima occurs when sin Ə = λ/a .
aT
First minima
Central maxima
Q1 Find the angle at which the first minima occurs using microwaves of wavelength 3 cm when directed towards a gap of:1) 6cm2) 4cm
Ə
It can be shown that the first minima occurs when sin Ə = λ/a .
aT
First minima
Central maxima
Q1 Find the angle at which the first minima occurs using microwaves of wavelength 3 cm when directed towards a gap of:1) 6cm2) 4cm
Q2 Find the angle at which the first minima occurs using lightwaves of wavelength 500 nm when directed towards a pupil of diameter:1) 6mm2) 4mm
Ə
D
D
Points to note: * central fringe is twice as wide as the other fringes * intensity decreases from the centre * Central Fringe width W = λ/a x 2D
D
Points to note: * central fringe is twice as wide as the other fringes * intensity decreases from the centre * Central Fringe width W = λ/a x 2D
D
Blue light has narrower fringesSo cameras and microscopes
can see more detail using blue filters
Visit :http://www.phys.hawaii.edu/~teb/optics/java/slitdiffr/
WAVES
For first minimum sin a
Or for small angles in radians
a
a = width of the gap
How do you get the minima
a
Q First minima
wave trains arrive in phase at the central maxima.
λ
λ/2
A
B
C D
Q
AQ is λ/2 longer than CQ so is out of phase by π giving destructive interferenceCorresponding points along AB which are λ/2 apart also causedestructive interference.
How do you get the minima
a
Q First minima
wave trains arrive in phase at the central maxima.
λA
B
C
Q
How do you get the minima
a
Q First minima
wave trains arrive in phase at the central maxima.
λ
λ/2
A
B
C D
Q
AQ is λ/2 longer than CQ so is out of phase by π giving destructive interferenceCorresponding points along AB which are λ/2 apart also causedestructive interference.
How do you get the minima ?
a
Q First minima
λ
λ/2
A
B
C D
Q
AQ is λ/2 longer than CQ so is out of phase by π giving destructive interferenceCorresponding points along AB which are λ/2 apart also causedestructive interference.
CD = λ = a sinƏ 2 2
λ = a sinƏ λ = sinƏ a
Ə
The double slit pattern is superimposed on the much broader single slit diffraction pattern.
The bright central maximum is crossed by the double slit interference pattern, but the intensity still falls to zero where minima are predicted from single slit diffraction. The brightness of each bright fringe due to the double slit pattern will be “modulated” by the intensity envelope of the single slit
pattern.
Diffraction by a Double Slit
The double slit fringes are still in
the same placeSingle slit pattern
Double slit pattern
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Experimental observations from the double slit
i) For a pair of slits 0.5 mm apart:
λ red » λ blue
ii) Using white light, fringes appear from all the various wavelengths present and do not overlap exactly, hence coloured fringes
* Inner fringes are tinged with blue on the inside and red on the outside
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Experimental observations from the double slit cont’d
iii) Fringes obtained using slits 0.5 mm apart drawn with different widths
(a) (b)
(a) thin slits
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Experimental observations from the double slit cont’d
iii) Fringes obtained using slits 0.5 mm apart drawn with different widths
(a) (b)
(a) thin slits
The double slit interference pattern is modulated
by the single slit pattern
Diffraction is the spreading of wavefronts around corners and obstacles.
If the slit gets narrower diffraction increases.
If the wavelength increases diffraction increases.
Experimental observations from the double slit cont’d
iii) Fringes obtained using slits 0.5 mm apart drawn with different widths
(a) (b)
(a) thin slits (b) thick slits
The double slit interference pattern is modulated
by the single slit pattern
Missing fringes