1 Reflection of Light by Spherical Mirror
Reflection of Light by Spherical Mirror
Spherical Mirror
- Concave spherical mirror − A spherical mirror whose reflecting surface is towards the centre of the sphere is called concave spherical mirror.
- Convex spherical mirror − A spherical mirror whose reflecting surface is away from the centre of the sphere is called convex spherical mirror.
Focal Length of Spherical Mirror
- Principal focus (F) − The point at which a narrow beam of light incident on the mirror parallel to its principal axis after reflection from the mirror meets or appears to come from is called the principal focus of the mirror.
- Focal length − The distance between the pole and the principal focus of the mirror is called the focal length (f) of the mirror.
- For both concave and convex spherical mirrors,
Where,
f → Focal length of the mirror
R → Radius of curvature of the spherical mirror
New Cartesian Sign Conventions
Mirror Formula
The above figure shows the ray diagram for image formation by a concave mirror.
In figure, triangles and ENF are similar.
As the aperture of the concave mirror is small, the points N and P lie very close to each other.
∴NF ≈ PF and NE = AB
Since all the distances are measured from the pole of the concave mirror, we have
Also, triangles ABP and are similar.
From equations (i) and (ii), we obtain
Applying the new Cartesian sign conventions, we have
PA = − u (distance of object is measured against incident ray)
= − v (distance of image is measured against incident ray)
PF = − f (focal length of concave mirror is measured against incident ray)
Substituting these values in equation (iii),
We have
or
The above relation is called mirror formula.
- Relation betweenu, v, and R
, we have
- Linear magnification − The ratio of the size of the image formed by a spherical mirror to the size of the object is called the linear magnification produced by the spherical mirror.
It is denoted by m.
Where,
I → Size of the image
O → Size of the object
In the above figure, triangles ABP and are similar.
Applying the new Cartesian sign conventions, we have
= − I (height is measured downwards)
AB = +Â OÂ (height is measured upwards)
PA = − u (distance is measured against incident ray)
= − v (distance of image is measured against incident ray)
∴The above equation becomes
Note:Â The expression for magnification is same, both for the concave and convex mirrors.