PHYSICS 220/230
Lab 8: 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 computationally and experimentally.  The following reference link provides the relevant equations: Geometric Optics

The applet below allows you to simulate standard optical elements (lenses, mirrors, sources, and objects) and observe the ways that light rays propagate through these elements.  You should conduct a simulation with this applet immediately before each of your real experiments to visualize how the principal rays converge and form the image that you will observe.

 

I. Converging Lenses

  1. Place a lens on the simulation screen by clicking the lens button and then clicking a position on the principal axis.  Now put an object on the screen by clicking the object button and then selecting a position on the screen.  You can reposition the lens or the object by clicking and dragging.  When the lens is selected, you can also click and drag the focal point to adjust the focal length of the lens.  Play with these parameters and describe how the image position and size depend on the position of the object.
  2. Now place the light source, the thin converging lens, and the screen in holders along the experimental 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 enlarged, 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 = + 6 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)

 

  1. 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

  1. Clear the simulation screen (click Clear All) and add a mirror and an object.  Observe and record how the image position and size depend on the object position.
  2. Repeat experimental 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.

Trial l

Trial 2

(1) source position
 
 
(2) mirror 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

  1. Simulate a concave lens by adding a lens and then dragging the focal point through the lens.  Place an object on the screen and describe the image that is formed.  How could you view this image? On a screen?  With your eye?  Now add a converging lens between the object and the diverging lens.  Can you configure this combination to produce an image that could be viewed on a screen?  How can you do this?
  2. Since negative or diverging lenses do not form REAL images of REAL objects, use the thin converging lens to set up an experimental VIRTUAL OBJECT for the diverging lens. Your setup should be as follows:

DIVERGING LENS: Power = -2 Diopters

Trial l

(1) source position
(2) converging lens position
(3) screen position without lens 2
(4) diverging 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

  1. Simulate a convex mirror by adding a mirror and then dragging the focal point through the mirror.  Add an object and describe the image.  Now add a converging lens and observe how the trajectories of the optical rays change as you vary the positions of the lens and object.  Why do multiple images appear and how are they numbered?
  2. Experimentally determine the focal length of the convex mirror by using it in conjunction with the thinner 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)

 


OpticsApplet version 4 was written by Wolfgang Christian.