Week 10 (Nov. 2-6)

Read: (Chap. 13) and (Chap. 14)

PHY 202 Lecture: Geometric optics
Homework:
  1. Focal length of a spherical mirror (202 students only: Ex. 12.6)
  2. The superposition principle and wave interference (Ex. 14.1)
  3. Huygens principle and wave diffraction (Ex. 14.2).

Laboratory: Geometric optics laboratory.

Part 1: The thin lenses

  1. Place a converging (double convex) lens with a focal length of between 15 and 50 cm in a lens mount on a carriage near the center of the optical bench. The lens should remain at the center of the optical bench for most of this lab.
  2. Place the light source on a carriage on one side of the lens and the screen on a carriage on the other side.
  3. Place the light source as far away from the lens as possible. Move the screen until the images comes into focus on the screen. There will be a range of image distances that yield an acceptable focus; this is due to spherical aberration. That is: the outer edge of the lens does not focus the light rays to the same point as the center of the lens does. Spherical aberration is most pronounced for very fat (short focal length) lenses.
  4. Measure the length of the arrow used as the object and record it as the object size. Record the object distance, d0, and the image distance, di, as well as the image size. The image and object distances should be measured from the center of the lens. Do this for at least ten different image and object distances.
  5. Plot the data in a manner that yields a straight line. For a straight line, y = mx + b. Therefore, plot the inverse of the image distance (ordinate) versus the inverse of the object distance (abscissa). Determine the focal length from the intercepts with both the x-axis and the y-axis. Hint: relate ( 1 / di ) = - (1/ d0 ) + ( 1 / f ) to y = mx + b.
  6. Calculate the magnification for each data point, using both the formula (magnification) = (image size) / (object size) and (magnification) = - di / d0. Where must we place the object, in relation to the focal length, to get a magnified image?

Part 2: Fat lenses, apertures, and f-ratio.

  1. Now swap out your thin lens with a fat (focal length of perhaps 5 cm) double convex lens. Focus the image form the light source on your white screen.
  2. The f-ratio of an optical system is the (dimensionless) ratio of the focal length of the lens to the diameter of the lens. Calculate the f-ratio of your lens. Hint: if you are not sure of the focal length of the lens, you’ll need to measure it at this point.
  3. Now put a small circular aperture right next to the lens between the light source and the lens; this reduces the effective diameter of the lens to the aperture size. What do you notice about (i) the sharpness of the image, (ii) the brightness of the image?, and (iii) the depth of field (the range over which you get a focused image)? Record the f-ratio for this arrangement. Repeat this for several aperture size; for each take a picture of the image on the screen to document your results.
  4. Do some reading/research on f-ratio as it relates to photography. What does the f-ratio have to do with image brightness and depth of focus? Explain this briefly in your laboratory notebook.

Part 3: Spherical mirrors

  1. Place a clean (use methanol) concave mirror in a mount on a carriage at the end of the optical bench. You will need to angle the mirror so that it forms an image on a screen that is slightly displaced to the side of the light source.
  2. Place the light source as far away from the mirror as possible. Move the screen until the image is focused on the screen. Record the object distance and the image distance as well as the image size. The image and object distances should be measured from the vertex of the mirror. Due to spherical aberration and poor mirror quality, it may be difficult to obtain a sharp focus. You may determine a range of good focus and use the average distance.
  3. Move the light source a few centimeters closer to the mirror. Find the new position of the screen where the image is in focus. Repeat this for perhaps ten different image and object distances. Include positions where the image is larger than the object.
  4. Plot the data in a manner that yields a straight line. For a straight line, y = mx + b. Therefore, plot the inverse of the image distance (ordinate) versus the inverse of the object distance (abscissa). Determine the focal length from the intercepts with both the x-axis and the y-axis. Hint: relate ( 1 / di ) = - (1/ d0 ) + ( 1 / f ) to y = mx + b.
  5. What is the radius of curvature of the mirror? Is it equal to half the focal length?



Chapter 13 (3 videos):





Physics 2