Purpose: To verify the thin lens formula. To investigate the properties of a converging lens, including the magnification. To verify the object-image distance formula for spherical mirrors.

Discussion: The thin lens formula is,                  1/f = 1/d_o + 1/d_i

and the magnification formula is,                      m = h_i/h_o = -d_i/d_o

For a converging lens, f is assumed to be positive.  If the object is real, d_o is also positive.

Procedure:
1. Place the lamp near the zero end of the optical bench. The object will be the black arrow on the lamp cover.  Write down its position as x_o. You may keep the position of the object constant throughout the experiment.  Measure h_o the height of the object.

2. Position the recommended lens at some intermediate position x_L. Remember that in order to make a real image, the object cannot be too close to the lens.

3. By moving the white screen, determine x_i the position of the image.  Calculate the object distance [d_o = x_L - x_o] and the image distance d_i = [x_i - x_L]. Calculate 1/d_o and 1/d_i.

4. Measure h_i the height of the image. Note that an inverted image has a negative height! Calculate the observed magnification h_i/h_o and the theoretical magnification - d_i/d_o. Do they agree?  Calculate a percentage difference.

5. Repeat steps 2-4 for a range of possibilities. Make sure you cover the entire range of object distances which will create a real image!

6. Make a graph of 1/d_i versus 1/d_o. Do you get a straight line?  If so, what are the slope and intercept? According to the thin lens formula the slope should be -1 and the intercepts should be 1/f. Use your intercept to calculate the focal length f.

7. Calculate the percentage error in your slope.

8. Make a graph of the theoretical magnification - d_i/d_o on the vertical axis vs. the observed magnification h_i/h_o on the horizontal axis.  Make your axes with the same scale. Your data points should fall on a line inclined at 45° to the horizontal axis. Draw this line on your graph so that you can see how close to it your points are.

9. Set up the object, lens and screen so that you form an image on the screen. Predict what you would observe on the screen if you now cover the lower half of the lens with an opaque screen.
Perform this activity and record your observations.  How do you explain what you have observed?
Predict what you would see if you covered three-fourths of the lens with an opaque screen.
Perform this activity.  Record what you have observed. How do you explain your observation?