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fT
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/12
Acceleration:
tydt
yda sin2
max2
2
rc
aqEradiative 2
04
1
jsin4
12
2max
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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 – 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 – they ‘feed’ 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: Snell’s Law
sin (𝜃1 )=𝑣1𝑇 /𝑑𝜃1𝜃1
𝜃2
𝜃2
𝑣1𝑇
𝑣2𝑇
𝑑sin (𝜃1 )𝑣1
=sin (𝜃2 )𝑣2
sin (𝜃2)=𝑣2𝑇 /𝑑
sin (𝜃1 )𝑐/𝑛1
=sin (𝜃2 )𝑐 /𝑛2
Reflection and transmission
Total Internal Reflection
𝜃𝑔𝑙𝑎𝑠𝑠
𝑛𝑔𝑙𝑎𝑠𝑠≈ 1.5
=.75
𝜃𝑎𝑖𝑟
𝜃𝑔𝑙𝑎𝑠𝑠For small
W?
𝜃𝑎𝑖𝑟 ≈ si n−1 [𝑛𝑔𝑙𝑎𝑠𝑠 sin (𝜃𝑔𝑙𝑎𝑠𝑠 ) ]
=.96
=1.15
𝜃𝑎𝑖𝑟 ≈ 49 °
𝜃𝑎𝑖𝑟 𝑑𝑜𝑒𝑠𝑛′ 𝑡 𝑒𝑥𝑖𝑠𝑡…𝑛𝑜𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛
𝜃𝑎𝑖𝑟 ≈ 75 °
Thin Lenses How does the deflection angle depend on the height, ?
2 𝛿2y
𝛿=𝑦𝑓
𝑓
For converging lenses parallel rays cross the axis at the focal distance from the lens
𝛿y
When changes by factor of 2 change prism angle changes by factor of 2
𝛿∝𝜙
𝜃2+𝜃3=𝜙
𝜃1+𝜃4=𝛿+𝜙
For small angles, using Snell’s law
and
𝑛𝜃2+𝑛𝜃3=𝛿+𝜙𝑛(𝜃¿¿2+𝜃3)=𝛿+𝜙 ¿
𝑛𝜙=𝛿+𝜙𝛿=𝜙(𝑛− 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)
𝜃1
𝜙
𝜙
𝜃2
𝜃3
𝛿
𝜙
Deviation doesn’t depend on incident angle
𝜃4
Add to the 2nd perpendicular
Images
• Images are formed where rays intersect–Real image: rays of light actually intersect
–Virtual image: rays of light appear to intersect
Lenses• 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
• Converging lenses• Thickest in the middle
• Diverging lenses• Thickest at the edges
Focal Length of a Converging Lens
• The parallel rays pass through the lens and converge at the focal point
• Focal length is positive.
Focal Length of a Diverging Lens
• The parallel rays diverge after passing through the diverging lens
• The focal point is where the rays appear to have originated (focal length is negative)
Converging Lens,
• The image is virtual and upright𝑠
hobject
𝑠 ′h ′
image
𝑓
• 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
1𝑠𝑜
+1𝑠𝑖
=1𝑓