Reflection of light: Bouncing back of light rays after striking a surface in called as reflection.

Laws of Reflection:-

Angel of incidence = Angle of reflection  i.e.   ∠i = ∠r  

1. Incident ray, reflected ray and normal all lie in the same plane.

Spherical mirrors:-

A spherical mirror is a part of hollow sphere whose one side is reflecting and other side is opaque.

Types:

1. Concave mirror
2. Convex mirror

Few definitions:

1. Pole (P): centre of the mirror
2. Centre of curvature (C): is the centre of sphere of which mirror is a part.
3. Radius of curvature (R): radius of the sphere of which mirror is a part
4. Principal Axis : is the line joining C and P.
5. Principal Focus (F): is the point on the principal axis at which all rays parallel to principal axis converge or appears to converge after reflection from the mirror.
6. Focal length (f): is the distance between principal focus and pole.
7. Aperture: the diameter M₁,M₂ of spherical mirror is called aperture.

Relation between f and R :-

1. For concave mirror : consider a ray of light AB be incident on a concave mirror of small aperture.
   

   ∠ABC = i = angel of incidence

   ∠CBF = ∠ABC = i (law of reflection) 

   In ΔCBN; tan i = (BN/NC) = (BN/PC) = (BN/-R) ------(i)

   aperture is small

   ∴ NC ≈ PC ≈ -R

   In Δ FBN; tan 2 i = (BN/NF)= (BN/PF)=(BN/-f) -------(ii)

   Since aperture is too small ∴ i is too small

   ∴ tan i ≈ i,    tan2i ≈ 2i

   From (i)       i = (BN/-R),           from (ii) 2i = (BN/-f)

   ∴ (i/2i) = ((BN/R)/(BN/f)) = (f/R)           ==> f = R/2

2. For convex mirror:
   

   

In ΔCBN, tan i = (BN/NC) = (BN/PC) = (BN/+R) --------(i)

In ΔFBN, tan 2i = (BN/NF) = (BN/PF) = (BN / +f) --------(ii)

i is too small, ∴ tan i ≈ i  and tan 2i≈2i

From (i) i = (BN/R)        From (ii) 2i = (BN/f)

(i/2i) = ((BN/R)/BN/f)           ==> f = R/2

Uses of Spherical Mirrors:-

1. Concave Mirrors:-

1. Used in telescope.
2. Used by dentists and E.N.T specialist to examine patients.
3. Used as shaving mirrors, which gives an enlarged image of face.
4. Used in cinema projectors.

2. Convex Mirrors:-

1. Used in automobiles because it produces the image smaller in size so that the field of view is more.
2. Used as a reflector in street lamps. As a reflect, the light from the lamp diverges over a large area.

The sign conventions:

1. All the distances are measured from the pole of a mirror.
2. The distances measured in the direction of incident light are taken as +ve while those in opposite direction are taken –ve.
3. Distance measured upward and normal to principal axis are taken as +ve and those measured m normally down ward are taken –ve.