We had to identify what kind of mirror would be best and atwhich position. I was

Question

We had to identify what kind of mirror would be best and atwhich position. I was wondering if some one would tell me if I amon the right track? I was thinking that a concave mirror with theobject to be ignited positioned at center of curvature, doesthat sound right to anyone else? We had to identify what kind of mirror would be best and atwhich position. I was wondering if some one would tell me if I amon the right track? I was thinking that a concave mirror with theobject to be ignited positioned at center of curvature, doesthat sound right to anyone else?

Explanation / Answer

To ignite a fire using sunlight and a mirror, we want to maximize intensity on the object to beignited, where Intensity = Power/Area One way to maximize intensity is to direct as many light rays(or photons) as possible towards a given area A, such that thepower is maximum in that area, i.e., the energy/time = power ismaximum in that given area, where photons carry energy E = hf anddeliver this energy in some characteristic time t. --------- It seems best to use a concave mirrorbecause the mirror is converging, hence it converges lightrays (or photons carrying energy) into a focused image,as opposed to diverting the photons in separate directions. Next, consider the Ray Drawing rules for ray diagrams ofconcave mirrors: 1) Ray 1 is drawn from top of object, parallel to principalaxis, and is reflected thru focal point f. 2) Ray 2 is drawn from top of object, thru the focal point f(or as if coming from focal point if object distance is less thanfocal distance), and is reflected parallel to principal axis. 3) Ray 3 is drawn from top of object, thru the Center ofCurvature C, and is reflected back on itself. --- Note: All three rays are reflected (no refraction is mentionedhere), so the three reflected rays converge back to form an imagein front of the mirror, i.e. between the object and themirror (as opposed to behind the mirror which would be theresult of refraction). ---
Consider Ray 3: the light ray is drawn from top of object thruCenter of curv. C, and reflected back directly on itself. Now it seems that if an object was placed directly on thecent. of curv. C, then the top of the objects makes a downward linethru the point C, which is perpendicular to the principalaxis. In order for a reflection to occur, the mirror mustbend 90o around from the intersection of the mirror withthe principal axis. --- It seems position C would be a blindspot for Ray 3 in mostmirrors. --- Therefore, the object should be placedat the focal point to maximize intensity because most rays willpass through the focal point. Considering Rays 1 and 3 should pass through thetop of the object being ignited and bottom, respectably, where thebottom of the object is the focal point itself,that should allow the ends of the objects to receive photonbombardment causing absorption of energy and hopefully lead toignition.
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Consider a figure of the concage mirror diagram, drawingthe the Rays listed above, it will seem evident as themirror must curve 90o for ray 3 to reflect back onitself for the case of object at C, the mirror can however curveless than 90o for ray 2 to reflect back on itself forthe case of object at f, so a smaller mirror is feasable to causeignition at point f as opposed to a larger mirror that must curve90 or 180 to create max intensity at point C.

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