Physics 1230 “Light and Color”: Exam #1 Your full name:

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General  information:  This  exam  will  be  worth  100  points.    There  are  10  multiple  choice  questions  worth  5  points  each  (part  1  of  the  exam)  and  problems  worth  a  total  of  50  points  (part  2  of  the  exam).    There  will  be  no  partial  credit  for  the  multiple  choice  problems.  Your  answers  to  the  problems  should  be  on  the  same  pages  as  the  exam  assignment  in  the  provided  space  (you  can  use  the  reverse  sides  of  the  pages  if  you  need  more  space  and  for  calculations).      

Rules  for  the  exam:  The  exam  will  be  held  during  a  regular  class  period.  All  exam  solutions  need  to  be  turned  in  by  5PM.  You  can  use  a  calculator  and  a  single  8.5  x  11  sheet  of  paper  with  equations  or  notes.  The  paper  must  have  your  name  and  student  number  on  the  top  of  both  sides;  the  rest  of  the  sheet  may  be  in  any  format  that  you  choose.  If  you  are  eligible  for  special  considerations  because  of  a  disability,  you  must  bring  a  letter  from  the  CU  Office  of  Disability  Services.  The  letter  will  be  in  effect  for  the  entire  term,  and  you  need  submit  it  only  once  before  the  first  exam.  I  will  make  special  arrangements  on  a  case  by  case  basis.  You  may  be  excused  from  an  exam  because  of  a  medical  problem;  please  give  me  a  note  from  a  doctor  in  this  case  if  possible.  I  will  deal  with  these  situations  on  a  case  by  case  basis.  The  exam  solutions  will  be  posted  at  the  course  web  page  soon  after  the  exam.  The  exam  scores  will  be  posted  at  https://culearn.colorado.edu      

Equations: Lens equation io xxf111

+= , where f is focal length of a lens (positive for convex

converging lens), xo is distance from center of lens to object, xi is distance from center of lens to image (positive if on opposite side of lens from object)

 Magnification  equation:      M  =  si/so  =  -­‐xi/xo    ,  where    si  =  size  of  image  (perpendicular  to  axis),  s0  =  size  of  the  object  (in  direction  perpendicular  to  the  axis)  

Law  of  refraction:      The  amount  of  light  bending  at  an  interface  of  two  media  is  determined  by  the  law  of  refraction  (the  so-­‐called  Snell's  law):    ni  sinθi  =  nt  sinθt  ,  where    θi  =  angle  between  incident  ray  and  normal,  θt  =  angle  between  transmitted  ray  and  normal,  ni  and  nt  are  the  indices  of  refraction  in  the  medium  containing  the  incident  ray  and  in  the  medium  containing  the  transmitted  ray.    

Relationship  between  frequency  and  wavelength  of  light:      λ ·∙ν  =  c    λ = wavelength, ν = frequency, c = speed of light (3 x 108 m/s in empty space).

Critical angle & total internal reflection:

 n1  and  n2  are  the  indices  of  refraction  in  the  medium  containing  the  incident  ray  and  in  the  medium  containing  the  transmitted  ray,  respectively.    

Bending power of a lens: P = 1/f P  =  power  in  diopters,  f  =  focal  length  of  the  lens  in  meters  

 Combined  power  of  two  thin  lenses  in  contact:    P1  +  P2  =  P    P1  =  power  of  lens  1;      P2  =  power  of  lens  2;      P  =  power  of  combined  lenses  

 

Exam  Assignment,  Part  1  (multiple  choice  problems,  50  points  total):    1.1. A wavelength of 633 nm is numerically equivalent to (5 points) (*) 0.633 µm and 633 x 10-9 m () 0.633 mm and 63.3 x 10-8 m () 0.0633 m and 633 x 10-4 m () 6.33 mm and 63.3 x 10-5 m () none of the above 1.2. Using the speed of light in vacuum, calculate how long it takes a light signal to travel on a straight line from Denver to New York, a distance of 2,000 km. (5 points) (*) 6.67 x 10-3 s () 0.67 s () 6.67x 10-6 s () 3.3 x 10-3 s () 13.2 x 10-3 s 1.3. Radio Station KGNU broadcasts at a frequency of 88.5 MHz (88.5 x 106 Hz). The wavelength of this signal is about (5 points) (*) 3.4 m () 3.4 km () 34 m () 1.8 m () 1.8 km 1.4. Which of the following statements is true (choose only one answer)? (5 points)

(*) The magnification of a pinhole camera increases when the screen used to display the image is moved further away from the pinhole (leaving everything else the same). () The magnification of a pinhole camera increases when the object is moved further away from the pinhole (leaving everything else the same). () The image produced by a pinhole camera is always the same size as the object, but is inverted. () The magnification of a pinhole camera depends on the wavelength of the light that is used to illuminate the object. () The magnification of a pinhole camera depends on the size of the pinhole

1.5. If the index of refraction of a medium is 1.25, the speed of light in that medium is (5 points) (*) 240,000 km/s () 260,000 km/s () 220,000 km/s () 240,000 m/s () none of the above 1.6. The critical angle for total internal reflection at the interface between air and glass is (5 points)

() larger for blue light than for red light because the index of refraction for blue light in glass is larger

(*) smaller for blue light than for red light because the index of refraction for blue light in glass is larger () larger for blue light than for red light because the index of refraction for blue light in air is larger () smaller for blue light than for red light because the index of refraction for blue light in air is smaller () the same for blue light and red light

1.7. If a pulse of red light and a pulse of blue light travel in vacuum (5 points) () The red pulse travels faster because its index of refraction is smaller () The blue pulse travels faster because its index of refraction is larger (*) The two pulses travel at the same speed

() The relative speed depends on the exact wavelengths of the red and blue pulses () The relative speed depends on the polarization of the two pulses 1.8. If a light wave is traveling in vacuum and its period is doubled then (5 points) () its frequency and its wavelength both double () its frequency and its wavelength are both halved (*) its frequency is halved and its wavelength is doubled () its frequency is doubled and its wavelength is halved () its frequency and its wavelength both increase by the square root of 2 1.9. Two thin magnifying glasses each have the same focal length of 20 cm. What is the effective focal

length of the combined lenses when they are touching each other? (5 points) ( ) 5 cm, (*) 10 cm, ( ) 20 cm, ( ) 10 m, ( ) 1 cm

1.10. You are looking towards the sun while standing on Earth in the penumbra of the moon. At that moment you are seeing (5 points)

( ) A total eclipse of the sun (*) A partial eclipse of the sun ( ) A total eclipse of the moon ( ) A partial eclipse of the moon ( ) None of the above

Exam  Assignment,  Part  2  (50  points  total)

2.1. Electromagnetic waves propagate with well know velocity of 3  x  108  m/s  in  vacuum  (10 points).

(a) How far away is the moon if it takes 3 seconds for sunlight reflected from the surface of the moon to reach us (Show your work)?

distance  =  time  x  velocity.  Therefore,  distance  to  the  moon  =  3s  x  3  x  108  m/s  =  9  x  10

8  m  

 (b) If the index of refraction of glass is 1.5, what is the speed of light in glass? (Show your work)

Speed of light in glass = speed of light in vacuum/refractive index = c/n. So speed in glass = (3 x 10

8 m/s)/1.5= 2 x 10

8 m/s

2.2. Draw the Sun, Moon and Earth during (a) Lunar eclipse and (b) Solar eclipse, and label the various parts of the shadow in both cases (10 points). (a) Lunar eclipse

(b) Solar Eclipse

Earth Moon Sun

2.3. Explain why an observer sees a fish in water in a location different from its actual position. Show schematically how rays propagate from a fish to the observer’s eye. (5 points).

The observer sees the fish in a location different from its actual position because of light refraction at the water-air interface.

2.4. White light often splits into colors, as shown in the two examples below (10 points):

(a) Explain why white light splits into different colors after passing through a prism and a raindrop. How is this phenomenon called? (5 points for the part (a)).

Indices of refraction and velocities of light wave propagation in the prism are different for different colors in the visible spectrum. This results in different angles of refraction of light rays of different color at the air-prism and prism-air (or air-droplet and droplet-air) interfaces. This phenomenon of splitting of white light into light of different colors is called “light dispersion”.

(b) What can you say about the indices of refraction and velocity of waves corresponding to different colors propagating in the medium of a prism/raindrop (glass/water). (5 points for part (b)).

In the media such as water and glass, the index of refraction is the largest for the violet light and the smallest for the red light. In these media, red light propagates faster than violet light. In these media, the index of refraction decreases and the speed of light increases with increasing wavelength of light.

 

 

 

 

 

 

2.5. The lens shown below has focal distance f=10m. (10 points)

(a). Using two special rays find the image of the red arrow below and then use the 3rd special ray to verify that your result is correct.

(b) Knowing that the distance from the lens to the object (red arrow) is 15m (as marked above), use an appropriate equation and calculate the distance to the image of this arrow. Show your work.

We use the Lens  equation  io xxf111

+=    and  find  that  oi xfx111

−= .  Substituting  the  distances  into  

the  equation,  we  find  mmmmxi 301

1505

151

1011

==−=  and  then  the  distance  to  the  image   mxi 30= .  

 

 2.6.  The photo below show a demonstration with rays of light similar to what we had in class previously. There are no mirror surfaces and the materials used in the experimental demonstrations shown below are transparent. Explain the observations and step-by-step describe phenomena that make the light rays changing their propagation direction. (5 points).

 

This  demonstration  shows  refraction  and  total  internal  reflection  of  incident  light  rays  at  the  interfaces  of  transparent  media.  In  the  top  left  photo,  the  ray  is  refracted  at  the  air-­‐material  interface,  then  reflected  (because  of  total  internal  reflection)  at  the  material-­‐air  interface  and  then  again  refracted  at  the  material-­‐air  interface.  The  same  sequence  of  refraction/reflection/refraction  takes  place  at  the  bottom  left  photo.  The  two  right  photos  demonstrate  total  internal  reflection  at  one  of  the  material-­‐air  interfaces  and  also  straight  propagation  of  the  ray  incident  normally  to  the  air—material  interface  (without  changing  the  direction).