Reflection of Light by Spherical Mirrors: Overview, Questions, Preparation

Spherical mirrors are the mirrors whose surfaces resemble the shape of a sphere. Spherical mirrors are of 2 types:

1. Concave Mirrors: These are the mirrors whose surface of reflection are curved inside and converge the parallel rays (resemble the inner portion of the spoon).
2. Convex Mirrors: These are the mirrors whose surface of reflection are curved outside and diverge the parallel rays (resemble the outer portion of the spoon).

There are majorly two laws of reflection which the candidates need to be aware of:

First law of Reflection:

This law states that the angle of incidence will be equal to the angle of reflection.

Can be represented by the equation:

∠i=∠r

Where

i = angle between the incident ray and the surface (normal).

r = angle between the reflected ray and the surface (normal).

Second law of Reflection:

According to this law, incident ray, reflected ray and the normal are coplanar i.e. they should all lie in the same imaginary plane.

You need to be familiar with the key terms mentioned below in order to be able to solve numericals related to mirrors:

• Pole: Center part of the mirror’s surface.
• Center of Curvature: Center of the sphere of which the mirror is a part of.
• Radius of Curvature: Distance between pole and center of curvature.
• Principal Axis: Line passing through the pole and center of curvature.
• Focus: The point where the parallel rays converge/diverge.
• Focal Length: Half the radius of curvature i.e. distance between pole and focus.

For a concave mirror:

• Ray parallel to the principle axis passes through F and vice versa.
• Ray passing through center of curvature will be reflected back along the same path.
• Ray passing through the pole will be reflected according to the laws of reflection.

For a convex mirror:

• Ray parallel to the principle axis appears to come from the focus.
• Ray passing through center of curvature will be reflected back along the same path.
• Ray passing through the pole will be reflected according to the laws of reflection.

•       Real Image: When rays converge at a point
• Virtual Image: When rays appear to diverge at a point
• Erect Image: Image formed is same as the object.
• Inverted Image: Image formed is upside down as compared to the object.

Mirror Formula and Magnification

The mathematical representation of the mirror formula is $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

 

where

  U is object distance

 V is image distance

F = focal length

Note:

• Magnification $m=-\frac{v}{u}=\frac{h_i}{h_0}$ , with a negative sign for real images when object is in front of the mirror.
• F = R/2 (R = radius of curvature)

These mirrors are used in our day to day lives, with some common examples listed below:

Concave Mirrors:

• Car headlights
• Shaving mirrors
• Solar panel
• Telescope
• Dental mirrors

Convex Mirrors:

• Rear View mirrors
• Security mirrors
• Mirrors at the road corners
• Reflectors