You are lost in the wilderness, carrying only a piece of aluminum foil. Thanks t

Question

You are lost in the wilderness, carrying only a piece of aluminum foil. Thanks to diligent study in your biology class, you remember which mushrooms are poisonous, and you are able to pick others that won't kill you. Your talents in basket weaving also pay off magnificently, as you create a basket and devise a plan to line it with aluminum foil, making a solar cooker. Mmmm, roast mushrooms! The basket is a section of a sphere with radius 21.0 cm. How far from the bottom of the basket should you place the mushrooms to cook them most efficiently using the Sun's rays? Is the sphere shaped basket the best?

Explanation / Answer

In this case, the sun is the "object" and it can be consideredto be an infinite distance away from the concave sphericalmirror.   The rays from the sun are reflected from thesurface of the spherical mirror thru the focal point, F. Thefocal length of the spherical mirrror is R/2, where theradius R is given to be 21 cm.   Thus, the mushroomsshould be placed at the focal distance of 10.5 cm in order toreceive the maximum heating effect. The spherical mirror is NOT the best since not all of thesun's rays are focused exactly at F due to sphericalabberations. A parabolic mirror would eliminate these abberations and workbetter to cook the mushrooms faster.

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