Solving Spherical Mirror Homework: Focal Length & Point of Incidence

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The discussion centers on understanding the relationship between the focal length and the point of incidence in spherical mirrors. It explains that when the aperture of the mirror is small, the point of incidence (P') is nearly coincident with the pole (P), leading to the conclusion that the focal length (PF) is approximately equal to half the radius (R/2). The confusion arises from the geometric representation, where it is clarified that if P' is far from P, the distances FP and FP' differ significantly. However, as P' approaches P, the two distances converge, validating the focal length formula. Ultimately, the focal length of a spherical mirror is established as R/2 when the aperture is small.
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Homework Statement



In the attached picture ,
It has been explained in my book that
" I the apeture of the mirror is small, the point P'( ponint of incidence) is very close to the point P( pole) ,Then PF(focal length)= P'F
:. PF =Fc
or PF=1/2R"
I don't get it !
Plzzzz help!
 

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By geometry they have shown that Fc = FP'.
If P' is away from P, FP' cannot be equal to FP because it is not the radius of the spherical surface. But if P' is very close to P, FP is nearly equal ti FP'. And hence you can show that focal length of teh spherical surface is R/2.
 

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