Reflection & Refraction,Reflected Images

Lecture 24

Monday: 12 April 2004

Chapter 35 Images

“Bar at the Folies-Bergere”

By Edouard Manet - 1882

Physical Principles of DesignActivity for Class 24 Monday: 12

April 2004

“e/m Ratio for the Electron” J.J.Thomson-Experiment

Joseph John (“J.J.”) Thomson

J.J. Thomson1856-1940

J.J. Thomson was appointed in 1884 asthe third Cavendish Professor (head ofthe Cavendish Laboratory) at Cambridge,after James Clerk Maxwell and LordRayleigh. In 1899, his experiments withcathode ray tubes led him to postulate theexistence of a new particle with a ratio ofcharge to mass (e/m) far larger than thesame ratio for a positive hydrogen ion.

The word “electron” was coined in 1891 by G. Johnstone Stoney.

Today we will measure e/m for the electron.

Calculating Change in K.E.from Electric Potential (Review)

V = 50

V = 0

V = 100

initial

final

e

e

0UK o r UK V)e(VqU o r V)e(U

J106.1

)100()106.1()V)(e(K17

19

I f t h e e l e c t r o n s t a r t s a t r e s t ( o r v e r y c l o s e t o i t ) ,t h e n

Vevm 22

1

Magnetic Force on aMoving Charge (Review)

BvqF

q: charge of the particle (C; + or –)v:velocity of the particle (m/s)B:magnetic field (T) Force is at a right angle to velocity. Force is at a right angle to magnetic field.

Important: If q is negative, that reverses the direction of force.

The Radius of the Circle (Review)

v

r

F

A l t h o u g h t h e d i r e c t i o n s o f t h e v e c t o r s a r ec h a n g i n g , t h e m a g n i t u d e s s t a y t h e s a m e .

rv

mamF2

BvqF

rv

mBvq2

Bqvm

Bvqv

mr2

Apparatus for Measuring e/m

We will set Potential in tube (V). Current in coils (I).

We will observe Radius of circular

electron path (r).

We will calculate e/m.

The Cathode Ray Tube

Electrons

Electrons are randomly kickedout of the metallic cathode bythermal energy.

Once free of the metal, the electrons are accelerated througha potential difference of V from cathode to anode.

Analysis of Electron Acceleration

Electron Stream

pot = -V pot = 0

cathode anode UK V)e(U

Ve)]V(0[e

]V)[e(K

E l e c t r o n s h a v e v e r y l o w k i n e t i ce n e r g y w h e n t h e y l e a v e t h ec a t h o d e – e s s e n t i a l l y z e r o .

Vevm 22

1 o r

mVe2

v

Helmholtz Coils

MagneticField

H e l m h o l t z C o i l s a r e d e s i g n e d t o h a v e an e a r l y u n i f o r m ( c o n s t a n t ) m a g n e t i cf i e l d i n t h e c e n t e r . T h e f i e l d d i r e c t i o n i sa l o n g t h e a x i s o f t h e c o i l s . T h em a g n i t u d e i s p r o p o r t i o n a l t o I , t h ec u r r e n t . T h e f o r m u l a t o c a l c u l a t e t h i s i sa P h y s i c s 2 t o p i c , b u t f o r o u r c o i l s ,

I108.7B 4w h e r e B i s i n t e s l a a n d I i s i n a m p e r e s .

Derivation of e/m Formula

Be

vmr

Br

v

m

e

m

Ve2v

Br

V2

m

e

Br

V2m

e

Brm

Ve2

m

e

Br

V2

m

e o r22 Br

V2

m

e We set or observe all of the variableson the right side of the equation.

Experimental Procedure

1. Turn up V to get an electronbeam. Record V.

2. Turn up I (to make B) until theelectrons make a complete circle.Record I.

3. Observe r – use the mirroredscale in the rear.

3a. Or (easier): Adjust I until theelectrons just hit the far side ofthe tube. This is a known radius(5.5 cm). Record I.

4. Repeat three times with differentvalues of V.

Viewing the Electron Path