PHYSICS 220/230
Lab 9: Lenses and Mirrors

You have studied lenses and mirrors and the equations, sign conventions, and ray tracing techniques that allow you to find images in geometrical optics. We want to look at these phenomena experimentally and computationally.

I. Converging Lenses

Place the light source, a converging lens, and the screen in holders along the optical bench. Adjust their heights to be about the same. Fix the position of the source and lens, and then adjust the position of the screen until a sharply defined image is formed on it. For an image that is magnified, record all the positions as well as the size of the object and the image. Then, make the required calculations to complete the data in the following tables.

CONVERGING LENS: Power = + 7 Diopters

Trial l

(1) source position
(2) lens position
(3) screen position
(4) object size: h
(5) image size: h'
(6) source distance: p
(7) image distance: q
(8) f (from lens formula)
(9) f (from 1/P)
(10) compare (8) and (9)
(11) m = h' / h
(12) m = -q/ p
(13) compare (11) and (12)

 

 

 

Repeat this set of measurements and computations for the thicker positive lens. In this case make the image a diminished one. Incorporate that data into the following table.

CONVERGING LENS
Power = + 20 Diopters


Trial 2

(1) source position
(2) lens position
(3) screen position
(4) object size: h
(5) image size: h'
(6) source distance: p
(7) image distance: q
(8) f (from lens formula)
(9) f (from 1/P)
(10) compare (8) and (9)
(11) m = h' / h
(12) m = -q/ p
(13) compare (11) and (12)

 

 

 

 


II. Concave Mirror

Repeat measurements, similar to those in part I, for the concave mirror. Note that in these measurements the source and screen both face the mirror and both are on the same side of the mirror. Hence, the heights of the screen and mirror must necessarily be slightly different so the rays from the source can focus on the screen. Do two trials, one with a magnified image and one with a diminished image.

CONCAVE MIRROR

Trial l

Trial 2

(1) source position
(2) lens position
(3) screen position

(4) object size: h

(5) image size: h'

(6) source distance: p
(7) image distance: q

(8) f (from mirror formula)

(9) m = h' / h

(10) m = -q/p

(11) compare (9) and (10)

III. Diverging Lens

Since negative or diverging lenses do not form REAL images of REAL objects, use the thin converging lens to set up a VIRTUAL OBJECT for the diverging lens. Which lens combination will give you the best results (+7 or +20)?  Your setup should be as follows:

DIVERGING LENS: Power = -1.75 Diopters


Trial l

(1) source position
(2) converging lens position
(3) screen position without lens 2
(4) concave lens position
(5) screen position with lens 2
(6) source distance: p2
(7) image distance: q2
(8) f2 (from lens formula)
(9) f2 (from 1 / P2)
(10) compare (8) and (9)

IV. Convex Mirror

Determine the focal length of the convex mirror by using it in conjunction with the thin converging lens. First obtain a REAL image of the source using the lens alone. Interpose the mirror between the lens and the original image. Next, turn the screen around and move it between the lens and the mirror. Adjust the heights of the source, lens, and screen so the top of the screen covers the lower half of the lens and the REAL image can be seen on the screen. Move the screen and/or mirror to observe a sharp image on the screen. Record the data and calculations as before.

 

CONVEX MIRROR


Trial l

(1) virtual object position
(2) mirror position
(3) final screen position
(4) source distance p
(5)image distance q
(6) f (from mirror formula)

 

 

V. Simulations

LOGAL is a powerful and flexible program for investigating and simulating optical image formation with lenses and mirrors. We will try various options to reproduce what you did above and add some new investigations, but with the ability to change variables much more easily. Go to Programs on "Energy"  and click on 'Apps95'. Then click on 'Logal' and open 'Explorer.exe'. In the Optics lab files, select Optexp.lab. Make the viewing area larger so you can more accurately see what is happening. Answer the questions posed below with short answers that are to the point.

  1. Click on the Exploration 'Plane Mirror'.
    Click on 'Display Optic Rail - Yes'.
    Click on 'Show Images - Mark All'.
    Open the toolbox and put a Plane Mirror (2nd from left, bottom row) on the rail.
    Place an object (arrow) on the rail; make sure the object is smaller than the mirror.
    Click on GO (the running person) to see the image. Move the object around. What
    happens to the image
    ?
    Click on RESET (the kneeling person).
    Place a light source on top of the object. Click GO to see the ray . By grabbing the tail of
    the source, rotate the beam and watch the ray. Does the ray always follow the laws of
    optics as you know them
    ?
    Hold down the CTRL and ALT keys and grab the tail of the light source. Drag the tail to
    the right until the number of rays is three. Click GO to see these rays and how they
    form the image.
    Click 'Toggle Screen On/Off'. Drag the screen until it is on top of the image. What do you
    see
    ? What kind of image is this?
    Click 'Toggle Screen On/Off'.
  2. Clear the Optic Rail by dragging all the objects to the trash.
    Add a concave mirror (5th from left, bottom row) to the rail.
    Place an object (arrow) on the rail; make sure the object is smaller than the mirror.
    Repeat the exercises from part a), staying outside the focal point.
    Then remove the light source.
    Then grab the object and go up to and inside the focal point. What happens?
    Add a light source and drag the ray around to see the effect. Do the principal rays follow
    the rules that we discussed in class
    ?
    Click 'Toggle Screen On/Off'. Determine the kind of image you have.
  3. Clear the optic rail and add a convex mirror (6th from left, bottom row).
    Place an object (arrow) on the rail; make sure the object is smaller than the mirror.
    Repeat the above exercises listed in b).
  4. Click 'Explorations'.
    Click 'Real and Virtual Images'.
    Click 'Display Optic Rail - Yes'.
    Add a convex lens (3rd from left, bottom row).
    Place an object (arrow) on the rail; make sure the object is smaller than the lens.
    Repeat the above exercises listed in b).
  5. Clear the optic rail and add a concave lens (4th from left, bottom row).
    Place an object (arrow) on the rail; make sure the object is smaller than the lens.
    Repeat the above exercises listed in b).