Is there any geometric proof on how spherical mirrors reflect light rays?

Question

If the LAW OF REFLECTION is obeyed, that is-- angle of incidence equals angle of reflection, then could it be proved geometrically that:

in spherical mirrors,
>a ray parallel to the principal axis will be reflected so that it passes or seems to pass through the focal point?

>a ray passing or seeming to pass through the focal point will be reflected parallel to the principal axis ?

how is it proved? (if you need to draw illustrations just send it to [e-mail], please...)

Answer 1

To elaborate on scafool's answer, the spherical mirror will focus well only for small-angle exposures. Spherical mirrors are just conveniently fabricable approximate substitutes for parabolic mirrors. I never understood why intro physics textbooks concentrate so much on spherical mirrors, when the focal formulas require such ugly approximations. Maybe it's because Newton used spherical mirrors in the "Opticks."

Anyhow, you should look up paraboloids, and think of a spherical mirror as an approximation to one of them. The approximation works because near the origin they are both quadratic.

Answer 2

for ne goemetrical proof jst do a thing use some calculas fanda u know about plane mirrors now jst asume tht a spherical mirror is made up of infinitisimally small plane mirrors n angle of incidence is equal to angle of reflection now if u need to do stg geometry abt focus n all tht stuff focus is jst practical asumption n tht asumed point is found by experiment only best of luck

Answer 3

Read a good text book. What you are stating is not true for spherical mirror.

Answer 4

those statements are not true for spherical sections, you are looking for parabolic reflectors I think.

Answer 5

Scafool is dead right. Those statements only hold for paraboloids.


Doug

Answer 6

rishika