Acceleration: Sinusoidal E/M field Sinusoidal Electromagnetic Radiation.

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 – 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

A ray travels from air to water

Example of Snell’s Law

𝜃1

𝜃2

𝜃𝑎𝑖𝑟=45 °

𝜃𝑤𝑎𝑡𝑒𝑟 ≈ ?33 °

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 °

Prisms and Lens

Convergent lens Divergent lens

Lens is flat in center and prism angle steadily increases as y increases

Prisms and Lens

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

𝛿=𝑦𝑓

y

𝑠𝑜 𝑠𝑖𝛼 𝛽

𝛼≈𝑦𝑠𝑜

𝛽 ≈𝑦𝑠𝑖

𝛼+𝛽=𝛿

𝑦𝑠𝑜

+𝑦𝑠𝑖

=𝛿=𝑦𝑓

1𝑠𝑜

+1𝑠𝑖

=1𝑓 Thin lens formula

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 real and inverted

𝑠hobject

𝑠 ′

h ′

image𝑓

Converging Lens,

• The image is virtual and upright𝑠

hobject

𝑠 ′h ′

image

𝑓

• Magnifying glass

Magnification

𝑓

Diverging Lens

• The image is virtual and upright

𝑠hobject

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

Plane or Flat Mirror

𝑠=−𝑠 ′ h=h ′Magnification

𝑠hobject

𝑠 ′

h ′image

Spherical Mirrors

• A spherical mirror has the shape of a segment of a sphere

• A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve

• A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve