Mirrors and lenses are covered f the text. We will begin covering lenses today. These are much more commonly used than curved mirrors, so this should be more relevant.
Lens equation 2013
Lenses• The Lens Equation– Calculating image location– Calculating magnification
The Lens Equation• Ray tracing is useful, but kind of tedious for allthese different cases, and accuracy requires veryprecise drawings.• We can verify ray tracing by using the lensequation• However, this will require some algebra.
Focal Length• Remember we defined the focal length for a lens• We also defined the sign of f. The focal length, f, isdefined as positive for converging lenses and negative fordiverging lenses.FFFocal length (f)
Lens Equation Quantities• We also need to define some other distances.Object distance, xoFocal length, fImage distance, xi• The object distance is positive for an object to the leftof the lens. The image distance is positive for a (real)image on the right of the lens. These quantities arenegative for the reverse situation. Be careful with this.
Lens Equation QuantitiesFocal length, fObject distance, xoImage distance, xi• The image distance is negative for a (virtual) image onthe left of the lens.
The Lens EquationObject distance, xoFocal length, fImage distance, xi
The Lens Equation• Given:• f = 10 cm• Object is 15 cm in front oflens: x0 = 15• Find:– Where is image and is itreal or virtual?• Solve equation for xi:– Substitute numbers forletters– Subtract 1/15 from bothsides– Arithmetic on calculator– Multiply by xi/0.033Image is 30 cm to the right of the lens andreal because xi is positive
The Lens EquationObject distance, 15 cmFocal length, 10 cmImage distance, 30 cmWe can verify our result is consistent with the result from ray tracing.Ray tracing does not give an exact numeric answer, because we can’tdraw all our lines perfectly. But we can verify our answers.
Lens Equation: Magnification• For objects and images above the axis, S is positive,for those below the axis, S is negative.Object distance, 15 cmFocal length, 10 cmImage distance, 30 cmObject size, SoImage size, Si
MagnificationObject distance, xoFocal length, fImage distance, xiObject size, SoImage size, SiMagnification is indicated by the letter M, and is negative for animage inverted with respect to the object, and positive for animage that is not inverted
MagnificationObject distance, 15 cmFocal length, 10 cmImage distance, 30 cmMagnification of -2 means the image is twice the size ofthe object and inverted.
Lens Equation Example• Given:• f = 10 cm• Object is 5 cm to left of lenscenter: x0 = 5• Find:– Where is image and is itreal or virtual?• Solve equation for xi:– Substitute numbers forletters– Subtract 1/5 from bothsides– Arithmetic on calculator– Multiply by xi/0.1Image is 10 cm to the left of the lens andvirtual because xi is negative