Question

how to determine kind of image in spherical mirrors in numericals​

Answer 1

Answer:

The incident ray is parallel to the optical axis. The point at which the reflected ray crosses the optical axis is the focal point. Note that all incident rays that are parallel to the optical axis are reflected through the focal point—we only show one ray for simplicity. We want to find how the focal length  FP  (denoted by  f ) relates to the radius of curvature of the mirror,  R , whose length is

R=CF+FP.(1)

The law of reflection tells us that angles  ∠OXC  and  ∠CXF  are the same, and because the incident ray is parallel to the optical axis, angles  ∠OXC  and  ∠XCP  are also the same. Thus, triangle  CXF  is an isosceles triangle with  CF=FX . If the angle  θ  is small then

sinθ≈θ(2)

which is called the “small-angle approximation”), then  FX≈FP  or  CF≈FP . Inserting this into Equation  1  for the radius  R , we get

R=CF+FP

=FP+FP

=2FP

=2f(3)

In other words, in the small-angle approximation, the focal length  f  of a concave spherical mirror is half of its radius of curvature,  R :

f=R2.(4)

Explanation: