Reflection

Laws of Reflection

(i) Angle of incidence is equal to the angle of reflection.

(ii) The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane.

 What are Spherical Mirrors ?

Mirrors whose reflecting surface is curved are called Spherical Mirrors.

There are two types of spherical mirrors:

(i) Convex Mirror

(ii) Concave Mirror

Common terms used while formation Ray Diagrams

1) Principal axis: 

• Straight line passing through the pole and centre of curvature in a spherical mirror is known as principal axis.
  

 2) Pole (P): 

• The centre of the reflecting surface in a spherical mirror is a pole. 
• It is represented by P.

 3) Aperture (MN): 

• The diameter of the reflecting surface is defined as aperture.
  

 4) Center of Curvature (C): 

• Reflecting surface in a spherical mirror has a centre, this is known as centre of curvature.
• The centre of curvature is centre of the hollow glass sphere of which the mirror was a part.
• Centre of curvature in convex mirror lies behind the mirror.
• Centre of curvature in concave mirror lies in front of the mirror.

 5) Radius of Curvature (R): 

• The radius of the reflecting surface of the spherical mirror is known as radius of curvature.
• The distance between the pole and the centre of curvature.
• It is represented by R.

 6) Principal Focus (F): 

 The point on principal axis where all the parallel light rays actually meet or appear to meet after reflection.

 7) Focal length (f): 

• The distance between the pole and the principal focus in a spherical mirror is known as focal length .
• It is represented by f.
  

 Note :  Relationship between focal length and radius of curvature: f = R/2

 Properties of Concave mirror

  

• Reflecting surface is curved inwards.  

• Converging mirror 

Properties of Convex mirror

• Reflecting surface is curved outwards.

• Diverging mirror

Representation of Images formed by Spherical Mirrors using Ray Diagrams.

(i)  A ray parallel to the principal axis, after reflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror.

 (ii) A ray passing through the principal focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, after reflection, will emerge parallel to the principal axis.

 (iii) A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path.

 (iv) A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror or a convex mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.

Ray Diagrams for Images formed by Concave Mirror

(i) Used in torches, search lights and vehicles headlights to get powerful parallel beam of light.

(ii) Concave mirrors are used by dentists to see large image of teeth of patients. (Teeth have to be placed between pole and focus).

(iii) Concave mirror is used as shaving mirror to see a larger image of the face.

(iv) Large concave mirrors are used to concentrate sunlight to produce heat in solar furnace.

Ray Diagrams of Images formed by Convex Mirror

Uses of Convex Mirror

(i) Convex mirrors are used as rear view mirrors in vehicles because

•  they always give an erect though diminished image.
•  they have a wider field of view as they are curved outwards.

(ii) Convex mirrors are used at blind turns and on points of merging traffic to facilitate vision of both side traffic.

(iii) Used in shops as security mirror.

Sign Convention for Reflection by Spherical Mirror

(i) The object is placed to the left of the mirror.

(ii) All distances parallel to the principal axis are measured from the pole of the mirror.

(iii) All distances measured in the direction of incident ray (along + X-axis) are taken as positive and those measured against the direction of incident ray (along – X-axis) are taken as negative.

(iv) Distance measured perpendicular to and above the principal axis are taken as positive.

(v) Distances measured perpendicular to and below the principal axis are taken as negative.

• Object distance = ‘u’ is always negative.

• Focal length of concave mirror = Negative

• Focal length of convex mirror = Positive

Mirror Formula

1/v + 1/u = 1/f

where, 

v = Image distance

u = Object distance

f = Focal length

• It is applicable for spherical mirrors in all positions of the object. 
  

Magnification of Spherical Mirrors

It is the ratio of the height of image to the height of object.

•  It is defined as relative extent to which an object is magnified in comparison to its object size.

m = Height of image/Height of object

 m = h_i/h_o

Also, 

m = -v/u

where 

m = magnification

h_o = height of the object 

h_i = height of the image. 

•  A negative sign in the value of magnification indicates that the nature of the image is real. 
• A positive sign in the value of the magnification indicates the virtual nature of the image.

 Conclusion:

 If ‘m’ is negative, image is real.

 If ‘m’ is positive, image is virtual.

 If h_i = h_o then m = 1, i.e., image is equal to object.

 If h_i > h_o then m > 1 i.e., image is enlarged.

 If h_i < h_o then m < 1 i.e., image is diminished.

• Magnification of plane mirror is always + 1.

‘+’ sign indicates virtual image.

‘1’ indicates that image is equal to object’s size.

• If ‘m’ is ‘+ve’ and less than 1, it is a convex mirror.

• If ‘m’ is ‘+ve’ and more than 1, it is a concave mirror.

• If ‘m’ is ‘-ve’, it is a concave mirror.

CBSE Grade 10 Science Chapter 10 - Light - Reflection and Refraction . Part 2 ( Refraction ) - visit here.