acceleration: sinusoidal e/m field sinusoidal electromagnetic radiation
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fT
f
/12
Acceleration:
tydt
yda sin2
max2
2
rc
aqEradiative 2
04
1
jsin4
12
2max
0
trc
qyEradiative
Sinusoidal E/M field
Sinusoidal Electromagnetic Radiation
Why there is no light going through a cardboard?
Electric fields are not blocked by matterElectrons and nucleus in cardboard reradiate lightBehind the cardboard reradiated E/M field cancels original field
Cardboard
1. Radiative pressure โ too small to be observed in most cases2. E/M fields can affect charged particles: nucleus and electrons
Both fields (E and M) are always present โ they โfeedโ each other
But usually only electric field is considered (B=E/c)
Effect of E/M Radiation on Matter
Effect of Radiation on a Neutral Atom
Main effect: brief electric kick sideways
Neutral atom: polarizes
Electron is much lighter than nucleus:can model atom as outer electron connected to the rest of the atom by a spring:
F=eE
Resonance
Radiation and Neutral Atom: Resonance
tEEy sin0
tFeEF yy sin0
Amplitude of oscillation will depend on how close we are to the natural free-oscillation frequency of the ball-spring system
Resonance
E/M radiation waves with frequency ~106 Hz has big effect on mobile electrons in the metal of radio antenna: can tune radio to a single frequency
E/M radiation with frequency ~ 1015 Hz has big effect on organic molecules: retina in your eye responds to visible light but not radio waves
Very high frequency (X-rays) has little effect on atoms and can pass through matter (your body): X-ray imaging
Importance of Resonance
In transparent media, the superposition can result in change of wavelength and speed of wavefront
Index of refraction of medium,
Depends upon wavelengthand properties of medium
Refraction: Bending of Light
Rays perpendicular to wavefront bend at surface
A ray bends as it goes from one transparent media to anotherRefraction: Snellโs Law
sin (๐1 )=๐ฃ1๐ /๐๐1๐1
๐2
๐2
๐ฃ1๐
๐ฃ2๐
๐sin (๐1 )๐ฃ1
=sin (๐2 )๐ฃ2
sin (๐2)=๐ฃ2๐ /๐
sin (๐1 )๐/๐1
=sin (๐2 )๐ /๐2
A ray travels from air to water
Example of Snellโs Law
๐1
๐2
๐๐๐๐=45 ยฐ
๐๐ค๐๐ก๐๐ โ ?33 ยฐ
Reflection and transmission
Total Internal Reflection
๐๐๐๐๐ ๐
๐๐๐๐๐ ๐ โ 1.5
=.75
๐๐๐๐
๐๐๐๐๐ ๐ For small
W?
๐๐๐๐ โ si nโ1 [๐๐๐๐๐ ๐ sin (๐๐๐๐๐ ๐ ) ]
=.96
=1.15
๐๐๐๐ โ 49 ยฐ
๐๐๐๐ ๐๐๐๐ ๐โฒ ๐ก ๐๐ฅ๐๐ ๐กโฆ๐๐๐ก๐๐๐๐ ๐๐๐ ๐ ๐๐๐
๐๐๐๐ โ 75 ยฐ
Thin Lenses How does the deflection angle depend on the height, ?
2 ๐ฟ2y
๐ฟ=๐ฆ๐
๐
For converging lenses parallel rays cross the axis at the focal distance from the lens
๐ฟy
When changes by factor of 2 change prism angle changes by factor of 2
๐ฟโ๐
๐2+๐3=๐
๐1+๐4=๐ฟ+๐
For small angles, using Snellโs law
and
๐๐2+๐๐3=๐ฟ+๐๐(๐ยฟยฟ2+๐3)=๐ฟ+๐ ยฟ
๐๐=๐ฟ+๐๐ฟ=๐(๐โ 1)
So the deviation angle is independent of the
; is the incident angle (air to glass)
; is the refracted angle (air to glass)
; is the refracted angle (glass to air)
; is the incident angle (glass to air)
๐1
๐
๐
๐2
๐3
๐ฟ
๐
Deviation doesnโt depend on incident angle
๐4
Add to the 2nd perpendicular
๐ฟ=๐ฆ๐
y
๐ ๐ ๐ ๐๐ผ ๐ฝ
๐ผโ๐ฆ๐ ๐
๐ฝ โ๐ฆ๐ ๐
๐ผ+๐ฝ=๐ฟ
๐ฆ๐ ๐
+๐ฆ๐ ๐
=๐ฟ=๐ฆ๐
1๐ ๐
+1๐ ๐
=1๐ Thin lens formula
Images
โข Images are formed where rays intersectโReal image: rays of light actually intersect
โVirtual image: rays of light appear to intersect
Lensesโข A lens consists of a piece of glass or plastic,
ground so that each of its two refracting surfaces is a segment of either a sphere or a plane
โข Converging lensesโข Thickest in the middle
โข Diverging lensesโข Thickest at the edges
Focal Length of a Converging Lens
โข The parallel rays pass through the lens and converge at the focal point
โข Focal length is positive.
Focal Length of a Diverging Lens
โข The parallel rays diverge after passing through the diverging lens
โข The focal point is where the rays appear to have originated (focal length is negative)
Converging Lens,
โข The image is virtual and upright๐
hobject
๐ โฒh โฒ
image
๐
โข Magnifying glass
Magnification
PhotolithographyA photomask is imaged onto the surface of a semiconductor substrate in the production of an integrated circuit. The mask is 0.25 m in front of a lens (0.25m), and the focal length of the lens is 0.05m. What should be the distance of the semiconductor surface behind the lens, ?
Choice (m)
A 0.05
B 0.0625
C 0.01
D 0.125
E 0.25
1๐ ๐
+1๐ ๐
=1๐
Spherical Mirrors
โข A spherical mirror has the shape of a segment of a sphere
โข A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve
โข A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve