1Lec. 9: Ch. 3 ‐ Geometrical Optics1. Virtual images2. Spherical mirrors, ray tracing3. Spherical lenses, ray tracingThin lens approximation3 formulas4. Aberrations of lensesWe did this1We are hereTo change your iClicker frequency, turn on your iClicker. Hold down on the power button until the power light blinks. Then hit DC. You should see a green light indicating that you have changed the frequency. We covered 32 of these viewgraphs. We skipped 14 and 15 for now.Real image made by a concave mirror(demonstration)CenterFocalpointMirrorsurfaceAxisABCReview ray tracing: convex and concave mirrorsConvex mirror: Concave mirror:(alternatively, arrow could be closer to mirror than F) Demo: blackboard optics3 rays:1. Start parallel to axis, thenbends thru an F2. Thru C, no bend3. Starts bent thru an F,becomes parallel 3Review ray tracing: convex and concave lensesConvex lens as a magnifier:(alternatively, could be a projection lens) Concave lens:(demagnifier) Demo: lenses and vugraf projector3 rays:1. Start parallel to axis, then bends thru an F2. Thru the middle, no bend3. Starts bent thru an F, becomes parallel 4Review: Ray tracings (1 to 4)5Review: Ray tracings (5 and 6) 6Here is one example of how to use the lens eqnwith a converging lens• Given:• f = 10 cm• Object is 15 cm in front of lens: x0 = 15• Find:– Where is image and is it real or virtual?• Solve equation for xi:– Substitute numbers for letters– Subtract 1/15 from both sides– Arithmetic on calculator– Multiply by xi/0.033—= —+ —11 1fxoxi10 151510—-—= —11 1xi0.033 = —1xixi= — = 30 cm1.033Image is 30 cm to right of center of lensand is real because xiis positiveHere is a sketch to show the previous result• We can verify our result by ray‐tracingf = 10xo= 15xi= 30Here is an example of how to use the lens eqnwith a diverging lens (see Fig. 3.28)• Given:• f = —5 cm • NOTE, THE FOCAL LENGTH OF A DIVERGING LENS IS NEGATIVE• Object is 12 cm in front of lens: x0 = 12• Find:– Where is image and is it real or virtual?• Solve equation for xi:– Substitute numbers for letters– Subtract 1/12 from both sides– Arithmetic on calculator– Multiply by xi/(‐0.283)—= —+ —11 1fxoxi-512—-—= —12-511 1xi-0.283 = —1xixi= — = -3.53 cm1-0.283Image is 3.53 cm to left of center of lensand is virtual because xiis negativeReview: Rules for mirror ray tracing• Rule 1 for mirrors: All incident rays parallel to the axis are reflected so that they appear to have come from the focal point F.• We also see that a ray coming in along a radius will have a zero angle with the normal (it IS a normal), so its reflected back on itself.• Rule 2 for mirrors: Incident rays coming toward the center of curvature, C, are reflected back onto themselves.• Notice that if I turn the reflected ray around, so that it is an incoming ray, it goes out parallel to the axis (turn around the paraxial ray so it goes out). Let’s call this rule 3:• Rule 3 for mirrors: Incident rays headed for F are reflected so that they are parallel to the axis. This is simply rule 1 with the rays turned around so the outgoing ray is the incoming ray and vice versa.10Review: Rules for ray tracing lenses• Rule 1. A ray parallel to the axis is deflected through F' (or as though it came from F'). Hint: In either case, the point F' will be on the ruler edge.• Rule 2. A ray through the center of the lens is not bent.• Rule 3. A ray from F (extension may be necessary) is deflected parallel to the axis.Rule 3 is rule 1 with a reversed path, just like for mirrors. You may have to extend the edge of the lens or the rays to apply the rules. 1112Lec. 9: Ch. 3 ‐ Geometrical Optics1. Virtual images2. Spherical mirrors, ray tracing3. Spherical lenses, ray tracingThin lens approximation3 formulas4. Aberrations of lenses12We are hereDCTo change your iClicker frequency, turn on your iClicker. Hold down on the power button until the power light blinks. Then hit DC. You should see a green light indicating that you have changed the frequency.Compound Lenses• Can have less aberration.• A modern lens can have 16 elements and can “zoom”. 13“stop”Reduces aberrationImage planeFresnel LensUsed in lighthouses 14Fresnel stage lightLighthouse lens15http://sandiartfullyyours.com/NewFiles/lighthouse3/images/Ponce%20Fresnell.jpgWeb tutorials with Java Applets• Useful web links on curved mirrors• http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html• http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html• http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html• http://micro.magnet.fsu.edu/primer/java/mirrors/convex.html• Useful web links on lenses• http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html• http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html• http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html• http://micro.magnet.fsu.edu/primer/java/lenses/d iverginglenses/index.html• http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html16161717Lec. 8: Ch. 3 ‐ Geometrical Optics1. Virtual images (review)2. Spherical mirrors3. Spherical lenses3 formulas4. Aberrations of lensesWe are here17Aberrations• Field curvature• Off‐axis aberration• Spherical aberration• Distortion• Chromatic aberration18Aberration: field curvature19Image does not lie in one planeOff axis aberrationEdges of images are less clear. 20Demo with lens and bulbSpherical aberrationRays at the edge focus closer to the mirror21Demo with lens, not mirrorAberrations: Distortion22Demo with overhead and small lensesChromatic Aberration23Demo with lens and bulb24Concept Question 1In this case, the image is:Eye sees an image here.A) VirtualB) RealDC25Concept Question 1In this case, the image is:Eye sees an image here.A) VirtualB) RealReal because the light rays really go through the image. You can put a screen there to see it.Concept Question 226screenlensmask12Two point sources of light are imaged onto a screen by a converging lens. The images are labeled 1 and 2. You slide a mask over the left half of the lens. What happens to the images?A) Image 1 vanishesB) Image 2 vanishesC) Something else happensConcept Question 227screenlensmask12Two point sources of light are imaged onto a screen by a converging lens. The images are labeled 1 and 2. You slide a mask over the left half of the lens. What happens to the