Geometric Optics

 Diverging Lenses

 Seat Experiment

 Measuring Your Prescription  Most prescription eyeglasses use diverging lenses to correct for myopia or nearsightedness. Such lenses create a virtual image nearer to the viewer than the object at reduced magnification.

 Hold a pair of glasses in your hand at a FULL arm's length over evenly spaced long parallel lines (any ruled paper). By alternately look through one lens and then past it, raise and lower the glasses until the magnified image of the lines is one-half the size of the object. At this point, the image through the lens will show two lines apparently fitting into the space of one line viewed past the lens. If they're your glasses, you WILL need someone else to do the focusing on this looking over your shoulder. The more eye relief (distance from lens to eye of viewer) used the more accurate your measurements will be.
 Measure the distance from the lined paper to the center of the lens. This is do, and using this measurement and the thin lens equations, you can determine the lens power in diopters, also called the eyeglass prescription.

 Q1: Using the thin lens formulas, show that when M = + 1 / 2 for a diverging lens; d i = - d o / 2; and f = - d o . Attach your proof to the sheet, together with a rough ray sketch of this situation (show focal, parallel and chief rays).  Q2: Determine do for four separate eyeglass lenses. Use the relationship Power (in diopters) = 1 / f (in meters) to determine the eyeglass prescription in diopters.  As an example: if d o = 33 cm; P = -3.3D. Write the focal length and diopter equivalence for your four lenses on the sheet.  Q3: What would be the focal length of a -1.75D and a -1.25D lens? Q4: How would a +1.75D lens differ from a -1.75D lens? Q5: How would an optometrist characterize the vision of a person with these prescriptions?

 References

 Dudley, Scott C. (1999). How to quickly estimate the focal length of a diverging lens. The Physics Teacher 37(2), p94.

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