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COLLEGE PHYSICS PH 222-2A (MIROV) Sample Optics Problems

STUDENT NAME: ________________________STUDENT id #: ___________________________ ----------------------------------------------------------------------------------------------------------------------------------------

ALL QUESTIONS ARE WORTH 20 POINTS

------------------------------------------------------------------------------------------------------------------------------------------NOTE: Clearly write out solutions and answers (circle the answers) by section for each part (a., b., c., etc.)

Important Formulas:

Ch. 33. ELECTROMAGNETIC WAVES

1. Electromagnetic waves

0 0

s i n ( )s i n ( )

1

m

m

E E k x tB B k x t

EcB

2. Poynting vector

0

2

0

2

1 - t h e r a t e p e r u n i t a r e a a t w h i c h e n e r g y i s t r a n s p o r t e d

1 t h e t i m e a v e r a g e d r a t e p e r u n i t a r e a o r i n t e n s i t y

- t h e i n t e n s i t y o f t h e w a v e s a t d i s t a n c e r f r o m a p o i n t s4

a v g r m s

s

S E B

S I Ec

PIr

so u r c e o f p o w e r P

3. Radiation pressure

( f o r c e i n c a s e o f t o t a l a b s o r p t i o n )

2 9 f o r c e i n c a s e o f t o t a l r e f l e c t i o n b a c k a l o n g p a t h )

( r a d i a t i o n p r e s s u r e i n c a s e o f t o t a l a b s o r p t i o n )

2 ( r a d i a t i o n p r e s s u r e i n c a s e o f t o t a l r e f

r

r

I AFc

I AFc

Ipc

Ipc

l e c t i o n b a c k a l o n g p a t h )

4. Polarizing sheets

0 0

20 0

1 t r a n s m i t t e d i n t e n s i t y o f i n i t i a l l y u n p o l a r i z e d l i g h t o f i n t e n s i t y I2

c o s t r a n s i m m t e d i n t e n s i t y o f i n i t i a l l y p o l a r i z e d l i g h t o f i n t e n s i t y I

I I

I I

5. Reflection and refraction Law of reflection: The angle of incidence equals the angle of reflection;

Index of refraction: n cv m

;

WORK ONLY 5 QUESTIONS

Law of refraction (Snell’s law): s i ns i n

1

2

1

2

vv

or n n1 1 2 2s i n s i n ;

1. Total Internal Reflection Critical angle for total internal reflection for boundary between two materials (where n1>n2):

s i n cnn

2

1

;

Critical angle for material-air boundary (where n is the index of refraction of the material):

s i n c n

1 ;

2. Polarization by Reflection A reflected wave will be fully polarized, with its electric vector perpendicular to the plane of incidence, if it strikes a boundary at Brewster angle , where

1 2

1

t a nBnn

Ch. 34. IMAGES

1. Focal length of spherical mirror: 12

f r (f is positive for concave mirror, negative

for convex);

2. Spherical Mirror equation: 1 1 1 2p i f r

(p and i are positive if object or image is in

front of the mirror, negative if behind; f>0, concave; f<0, convex); 3. Spherical Refracting Surface:

1 2 2 1 ( s i n g l e s u r f a c e )n n n np i r

Where n1 is the index of refraction of the material where the object is located, n2 is the index of refraction of the material on the other side of refraction surface, and r is the radius of curvature of the surface.

4. Thin lens

1 2

1 1 1 1 1( 1 )np i f r r

(p is positive if object is on near side of lens, negative if on far side; i is positive if image is on far side of the lens, negative if on near side; f>0, convex; f<0, concave, a convex lens surface that faces he object has a positive radius of curvature, a concave lens surface that faces the object has a negative radius of curvature.

5. Lateral Magnification produced by a spherical mirror or a thin lens imp

(when m is positive image is upright; when m is negative image is inverted);

11. Angular magnification of magnifier: 2 5 c mmf

12. Overall magnification of compound microscope: 2 5 , s i s t h e t u b e l e n g t h

e o b

c m sM m mf f

;

13. Angular magnification of telescope: o b

e

fmf

Ch. 35 INTERFERENCE

1. Two-slit interference pattern (Young experiment): maxima: dsin=0, , 2,... minima: dsin=1/2, 3/2, 5/2,...;

2. Intensity in Two-Slit Interference 2

01 24 c o s ; w h e r e s i n2

I I d

3. Thin Film Interference 2 , c o n s t r u c t i v e i n t e r f e r e n c e

12 ( ) , d e s t r u c t i v e i n t e r f e r e n c e2

w h e r e m = 0 , 1 , 2 , 3 , . . ; = ; 0 o r 2

f

f

f

f

t m

t m

n

Ch. 36. DIFFRACTION

1. Single-Slit Diffraction

2

s i n , f o r m = 1 , 2 , 3 , . . . ( m i n i m a )

s i n( ) , w h e r e s i nm

a m

aI I

2. Circular Aperture Diffraction

s i n 1 . 2 2 , ( f i r s t m i n i m u m - c i r c u l a r a p e r t u r e )d

3. Rayleigh’s Criterion(resolution for a circular aperture):

1 . 2 2 ( R a y l e i g h 's c r i t e r i o n )R d

4. Double-Slit Diffraction 2

2 s i n( ) ( c o s ) ( d o u b l e s l i t )

w h e r e s i n , s i n

mI I

d a

5. Diffraction Grating

sin , for m=0,1,2,... (maxima)with half-widths of the lines given by

(half-widths),cos

The dispersion is given by cos

The resolving power R is given by

hw

avg

d m

NdmD

d

R Nm

1. X-Ray Diffraction

2 sin , for m=1,2,3,... (Bragg's law)d m

20(-3) +6

h’=hxM=12 cm

S’