Solving Spherical Mirror Homework: Focal Length & Point of Incidence

[1/2"]

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!

 

[rl.bhat]

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.

 

[kerimek]

As a scientist, it is important to understand the principles behind the concepts we are studying. In this case, we are looking at spherical mirrors and their focal length and point of incidence. It is important to understand that the point of incidence (P') is the point where the incoming light ray hits the mirror. The pole (P) is the center of the mirror.

When the aperture of the mirror is small, it means that the mirror is not very wide. This leads to the point of incidence (P') being very close to the pole (P). This is because the smaller the mirror, the closer the incoming light ray will be to the center of the mirror.

Now, let's look at the equation PF = Fc. This equation means that the distance from the point of incidence (P') to the focal point (F) is equal to the distance from the pole (P) to the center of curvature (C). In simpler terms, this means that the focal length (PF) is equal to the radius of curvature (Fc).

We can also look at the equation PF = 1/2R. This equation means that the focal length (PF) is equal to half the radius of the mirror (R). This is because the radius of curvature (Fc) is equal to twice the focal length (PF).

I hope this explanation helps you understand the concept better. It is important to remember that these equations are based on the assumption that the aperture of the mirror is small. If the mirror is not small, then these equations may not hold true. Keep exploring and asking questions to deepen your understanding.