Reflection rules of Spherical Mirrors

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.

Table of contents:

• ● Rule 1 : Incident ray travelling parallely to Principal Axis
• ● Rule 2 : Incident ray passing through the Principal Focus
• ● Rule 3 : Incident ray pssing through the Center of curvature
• ● Rule 4 : Incident ray falling on the Pole obliquely

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.

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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.

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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.

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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.

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