In the previous page we have seen different
components of spherical mirrors, such as,
Principal Focus, Center of curvature etc.
Now let us see how the reflected rays behave
when incident rays fall on a spherical mirror.
We are going to study four rules of reflection,
namely, Rule 1, Rule 2, Rule 3 and Rule 4,
w.r.t both concave and convex mirrors.
This is no convention that we have named the rules as Rule 1, Rule 2...,
rather those are just four types of behaviour
of the reflected rays.
When a light-ray falls on a mirror,
it is reflected back.
The falling ray is called an incident ray.
The point where the ray touches the mirror
is known as the point of incidence.
The path of the reflected ray depends upon
the nature of the incident ray and the type
of the mirror. Let us explore the
nature of the reflected rays for both concave and
convex mirror.
Rule 1 : Incident ray travelling parallely to Principal Axis
Rule 1 for concave mirror
For a concave mirror,
when an incident ray is parallel to the Principal Axis,
the reflected ray passes through the Principal Focus F.
For later reference, let us call this as Rule 1 for concave mirror.
Rule 1 for convex mirror
For a convex mirror,
when an incident ray is parallel to the Principal Axis,
the reflected ray appears to be coming
from the Principal Focus F.
The thick dashed yellow lines above on the right side are
virtual(imaginary) rays actually.
Rule 2 : Incident ray passing through the Principal Focus
Rule 2 for concave mirror
For a concave mirror, when an incident ray passes
through the Principal Focus F,
the reflected ray travels parallel to the Principal Axis.
This is just the inverse of Rule 1; let us call it Rule 2 for concave mirror.
Rule 2 for convex mirror
For a convex mirror, when an incident ray seems to pass
through the Principal Focus F (incident ray extended),
the reflected ray travels parallel to the Principal Axis.
Note that the incident ray seems to pass
through the Principal Focus F, but actually does not travel
beyond the reflective surface.
The thick dashed yellow lines above on the right side are
virtual rays.
Rule 3 : Incident ray pssing through the Center of curvature
Rule 3 for concave mirror
When an incident ray passes
through the Center of Curvature C,
the reflected ray will return back through the same path.
This means it will reflect back through the incident path.
Let us call this as Rule 3 for concave mirror.
Rule 3 for convex mirror
When an incident ray seems to travel
through the Center of Curvature C,
the reflected ray will return back through the same path.
In such cases, incident path and reflection path are the same.
The dashed yellow lines above are virtual rays.
Rule 4 : Incident ray falling on the Pole obliquely
Rule 4 for concave mirror
When an incident ray falls on the Pole obliquely,
the reflected ray will make the same angle with
the Principal Axis as the incident ray has made.
In the above case, both the incident and
reflected ray have made an angle of θ
with the Principal Axis.
Rule 4 for convex mirror
Same as the case with concave mirror, let us call
this as Rule 4.
These are the rules followed by reflected rays
for a concave and convex mirror. They determine
the size, nature and position of the formed image
after reflection.
To understand how the images are formed, see the next page.
Summary: Four rules of reflection
01 -
When incident ray travels parallel to the Principal Axis,
for concave mirrors, the reflected ray travels
through the Principal Focus.
For convex mirrors,
the reflected ray travels as if it is
coming from the Principal Focus.
02 -
For concave mirrors,
when incident ray travels through the
Principal Focus,
or for convex mirrors,
when incident ray seems to travel through the
Principal Focus,
the reflected ray travels parallel to the Principal Axis.
03 -
For concave mirrors, when incident ray
travels through the Center of Curvature,
or for convex mirrors when incident ray seems
to pass through the Center of Curvature,
the reflected ray travels back through the same(incident) path.
04 -
When incident ray falls on the Pole obliquely,
the reflected ray will make the same angle with
the Principal Axis as the incident ray has made. This is applicable
to both concave and convex mirrors.
