Drawing ray diagrams for bi-concave and bi-convex spherical by davebusters

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									Lab Activity: Spherical Mirrors and Thin Lenses
          In this lab you will use ray tracing to determine the images produced by spherical mirrors and
lenses. You will use the mirror equation and the thin lens equation to determine the position of the image as
well as the type of image and compare that with actual measurements you make. The mirror and lens
equations will be derived in lecture.


Introduction

    You can use any two rays starting on some point on the object and hitting the reflecting or
refracting surface to help you find the image produced. However, for spherical mirrors and lenses
there are three incident rays that are easier to draw than others and that we will therefore use for
ray tracing. These rays are called principal rays:

    1. A ray parallel to the principal axis.
    2. A ray through the focal point.
    3. A ray through the center of curvature (mirror) or through the optical center (thin lens).

     The principal rays are reflected/refracted differently depending on whether the
reflecting/refracting object is a convex/concave mirror or lens.




Part A: Ray Diagrams for Spherical Mirrors
    The three principal rays for converging (concave) mirrors:
    1. Any incident ray parallel to the principal axis is reflected through the focal point (which
       is located at ½ R where R is the distance from the mirrors center (or vertex) to the center
       of curvature C.
    2. Any incident ray which passes through the focal point is reflected parallel to the
       principal axis.
    3. Any incident ray which passes through the mirror’s center of curvature C (i.e. along the
       radius) is reflected back upon itself.


    The three principal rays for diverging (convex) mirrors:
   1. Any incident ray parallel to the principal axis is reflected as if it came from the focal point
       (which is located at ½ R behind the mirror’s surface where R is the distance from the
       mirror’s center (or vertex) to the center of curvature C.
    2. Any incident ray which is directed towards the focal point is reflected parallel to the
        principal axis.
    3. Any incident ray directed towards the mirror’s center of curvature C (i.e. along the radius)
        is reflected back upon itself.

Practice drawing ray diagrams: Finish the ray diagrams for the following concave and convex
mirror setups using the rules for diagramming as given above. Do this for
               a) an object located between C and F
               b) an object located beyond C
               c) an object located between V and F
for the concave mirror and the case given for the convex mirror.



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Lab Activity: Spherical Mirrors and Thin Lenses




                            C               F             V
                                    R
                                                    R/2




                            C               F             V




              C               F                 V




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Lab Activity: Spherical Mirrors and Thin Lenses




                                                V                    F                       C
                                                                                 R
                                                          R/2

Questions:
For each case give your answers to the following questions in the table below:
   1. Is the image larger or smaller than the object?
   2. Is the image upright or inverted?
   3. Is the image real or virtual?

               Object       Image         Image           Image         Image           Exp.
 Mirror
              location     location   larger/smaller upright/inverted real/virtual     Check

              between
               C&F
              (case a)


             beyond C
Concave
              (case b)


              between
               V&F
              (case c)


             in front of
Convex
              mirror 

A shaving mirror would be an example of a convex or a concave mirror? Where would you put
your face?


The spherical mirror on a car’s side mirror would be an example of a convex or concave mirror.
Explain the warning: “Vehicles in mirror are closer than they appear!”


Ask your instructor to show you the experimental setup for mirrors and check your findings
experimentally (check box in table when you are satisfied).

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Lab Activity: Spherical Mirrors and Thin Lenses
Quantitative:
                     concave mirror,    concave mirror,    concave mirror,      convex mirror
                     object between     object beyond C    object between
                          C&F                                   V&F
object distance d0
     (measured)
image distance di
     (measured)
   focal length f
     (measured)
   object size h0
     (measured)
   image size hi
     (measured)
magnification M
     (measured)
image distance hi
    (calculated)
magnification M
    (calculated)
   image size hi
    (calculated)
  from diagram,
       image
 larger/smaller?
from calculation,
       image
 larger/smaller?
  from diagram,
       image
upright/inverted?
from calculation,
       image
upright/inverted?
  from diagram,
       image
    real/virtual?
from calculation,
       image
    real/virtual?

Make sure everything makes sense! Calculations and ray tracing results should be in agreement.
All of the sign conventions are given at the end of this tutorial.




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Lab Activity: Spherical Mirrors and Thin Lenses
Part B: Ray Diagrams for Spherical Lenses

   The three principal rays for converging lenses:
  1. Any incident ray parallel to the principal axis passes through the focal point on the side of
     the lens that the ray emerges.
  2. Any incident ray which passes through the focal point and then through the lens emerges
     from the lens parallel to the principal axis.
  3. Thin lens approximation: any incident ray which passes through the optical center of the
     lens passes straight through the lens unrefracted.

   Practice drawing ray diagrams: Finish the ray diagrams for the following bi-convex lenses
   using the rules for diagramming as given above.




       Is the image real or virtual? Is the image magnified? Is it right side up or inverted?


       Sketch where your eye has to be located in order to see the image.

       Is the location of the image closer to or farther from your eye than the actual object?


       Design a quick experiment to verify your answer to the question above. Does your
       diagram match what you can empirically determine from experiment?



       What will happen to the location and magnification of the image if the object is moved
       toward the lens? (The magnification is the ratio of image size and object size.)


       What will happen to the location and magnification of the image if the object is moved
       toward the focal point?


       If the object is between the lens and the focal length, what type of optical instrument
       would we call this in everyday language? i.e. What would you use this set-up for?




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Lab Activity: Spherical Mirrors and Thin Lenses




     Is the image real or virtual? Is the image magnified? Is it right side up or inverted?


     Sketch where your eye has to be located in order to see the image.

     Is the location of the image closer to or farther from your eye than the actual object?


     Design a quick experiment to verify your answer to the question above. Does your
     diagram match what you can empirically determine from experiment?



     What will happen to the location and magnification of the image if the object is moved
     toward the focal point?



     What will happen to the location and magnification of the image if the object is moved
     toward infinity?



     If the object is farther from the lens than the focal length, what type of optical instrument
     would we call this in everyday language? i.e. What would you use this set-up for?



     Try and use this lens to project a real image of a very distant object onto a sheet of
     paper. You can use the outdoors as your distant object if it is light enough outdoors. If
     not, use a tall light source as your object. How many centimeters from the lens must you
     place the paper? What does the distance between the lens and the paper tell you about
     the focal length of the lens?




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Lab Activity: Spherical Mirrors and Thin Lenses
   The three principal rays for diverging lenses:
  1. Any incident ray parallel to the principal axis appears to come from the focal point on the
     side of the lens that the ray is coming from.
  2. Any incident ray which is directed towards the focal point on the other side of the lens
     emerges from the lens parallel to the principal axis.
  3. Thin lens approximation: any incident ray which passes through the optical center of the
     lens passes straight through the lens unrefracted.

Practice drawing ray diagrams: Finish the ray diagrams for the following bi-convex lenses below
using the rules for diagramming as given above.




       Is the image real or virtual? Is the image magnified? Is it right side up or inverted?


       Sketch where your eye has to be located in order to see the image.

       Is the location of the image closer to or farther from your eye than the actual object?


       Design a quick experiment to verify your answer to the question above. Does your
       diagram match what you can empirically determine from experiment?



       What will happen to the location and magnification of the image if the object is moved
       toward the focal point?



       What will happen to the location and magnification of the image if the object is moved
       toward infinity?




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Lab Activity: Spherical Mirrors and Thin Lenses




        Is the image real or virtual? Is the image magnified? Is it right side up or inverted?


        Sketch where your eye has to be located in order to see the image.

        Is the location of the image closer to or farther from your eye than the actual object?


        Design a quick experiment to verify your answer to the question above. Does your
        diagram match what you can empirically determine from experiment?



        What will happen to the location and magnification of the image if the object is moved
        toward the focal point?



        What will happen to the location and magnification of the image if the object is moved
        toward infinity?




Part C: The Lens Equation
         You have completed ray diagrams to locate the image produced by a lens. Now you will
use the lens equation to determine the position of a real image and make comparisons with actual
measurements. These equations will be derived in lecture.
                                   1       1        1                             di
              Lens Equation:                           Magnification: M 
                                   f       do       di                            do

Equipment Needed: (blue optics boxes)

        optics bench             light source             75mm converging lens
        crossed target           viewing screen           3 component holders




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Lab Activity: Spherical Mirrors and Thin Lenses
Procedure:
1. Set the viewing screen 40cm from the object (a lit crossed target). Place the lens between the
    object and viewing screen. Slide the lens back and forth until a clear image is viewed on the
    screen. Record: the object distance, the image distance, the object height and the image
    height.
2. Slide the lens further down the bench and try and produce another clear image on the screen
    with a different lens location. Again record: the object distance, the image distance, the
    object height and the image height.

Calculations:
1. Using the lens equation, the distance of 40cm from the image to the object and the focal
    length of the lens, calculate the two different positions of the lens which will produce an
    image on the screen. (You will have to solve for the roots of a quadratic equation – i.e. you
    will find two solutions)
2. Using the results from calculations part 1, determine the magnification of these two images.
3. Compare the calculations to the actual measurements in the chart below:

                    measurement 1       measurement 2          solution 1         solution 2

       do

       di

  M = -di/do

       ho                                                        XXXX               XXXX

       hi                                                        XXXX               XXXX

  M = -hi/ho                                                     XXXX               XXXX

How close are your measured values to your calculations? What is your percent error?




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Lab Activity: Spherical Mirrors and Thin Lenses
Part D: Lens Combinations
For the combinations of lenses below, find the final image, using ray tracing.

                    f1                  f1

                                                              f2         f2




                                                s
Suppose the focal lengths are 2.8cm and 1.25cm for the converging and diverging lenses, and that
the lenses are separated by 5.4cm. If the 1.3-cm object is placed 4.4cm in front of the converging
lens, find the final image, the total magnification and the image height of the final image. Make
sure you follow the sign conventions closely!




Questions:
1. According to your calculations, should your image be upright/inverted?


2. Should it be real/virtual?

3. Do the calculations and ray tracing agree qualitatively?

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Lab Activity: Spherical Mirrors and Thin Lenses
Equations:

Mirror Equation
1        1        1
             
 f       do       di

Thin Lens Equation
1        1        1
             
 f       do       di

Lens Maker’s Equation
1              1   1 
     n  1        
 f             R1 R 2 

Sign Conventions
The mirror equation and the thin lens equation work for both convex and concave mirrors and
lenses if you use the correct sign conventions.

Mirrors
Quantity                       Positive when                Negative when
Object location do             object is in front of mirror object is in back of mirror
                               (real object)                (virtual object)
Image location di              image is in front of mirror image is in back of mirror
                               (real image)                 (virtual image)
Image height hi                image is upright             image is inverted
Focal length f and radius R    mirror is concave            mirror is convex
Magnification M                image is upright             image is inverted


Thin Lenses
Quantity                       Positive when                    Negative when
Object location do             object is in front of lens (real object is in back of lens
                               object)                          (virtual object)
Image location di              image is in back of lens (real image is in front of lens
                               image)                           (virtual image)
Image height hi                image is upright                 image is inverted
R1 and R2                      center of curvature is in back center of curvature is in front
                               of lens                          of lens
Focal length f and radius R    converging lens                  diverging lens




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