Rules to draw ray diagrams & sign convention rules for spherical mirrors

RULES TO DRAW RAY DIAGRAMS FOR SPHERICAL MIRRORS

Rule 1:

The ray passing parallel to principal axis, after reflection passes through focus (or appears to be coming from focus in case of convex mirror)

Rule 2:

The ray passing through Focus (or appears to be passing through focus in case of convex mirror), after reflection becomes parallel to principal axis.

Rule 3:

The ray passing through principal axis comes back in the same path after reflection.

Rule 4:

The ray passing through centre of curvature (or appears to be passing through centre of curvature) comes back in the same path after reflection.

Why the ray comes back in the same path after reflection in Rule 3 & Rule 4?

Because as we know the ray passing through normal to the surface comes back in the same path. So, any ray passing through centre of curvature is passing through normal to the spherical surface as it makes an angle of 90⁰ with the tangent drawn to that point on the surface.

Note: the above rules are used to draw ray diagrams to understand the image formation by spherical mirrors. And the minimum number of rays required to show the formation of image is 2.

In ray optics

Object distance is denoted with ”u”

Image distance is denoted with “v”

Focal length is denoted with “f”

Radius of curvature is denoted with “R”.

Focal length is always half of the radius of curvature f=R/2 (or) R=2f

Sign convention rules for spherical mirrors:

i) All the distances must be measured from pole as pole acts as origin.

ii) The distances measured in the direction of incident rays are taken as positive and the distances measured in opposite direction to incident ray are taken as negative.

iii) The heights measured above principal axis are taken as positive and the heights measured below the principal axis are taken as negative.

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