Reflection at plane and spherical surfaces

Reflection at plane surfaces

(i) Reflection of Light 

When light rays strike the boundary of two media such as air and glass, a part of light is turned back into the same medium. This is called Reflection of Light. The wavelength and the velocity of the light wave remains the same

 

 455_Laws of reflection are obeyed at every reflecting surface.jpg

Laws of reflection are obeyed at every reflecting surface, i.e.

 

(ii) Laws of Reflection 

(a)       The incident ray (AB), the reflected ray (BC) and normal (BN) to the surface (SS') of reflection at the point of incidence (B) lie in the same plane. This plane is called the plane of incidence (or plane of reflection).

(b)       The angle of incidence (the angle between normal and between the reflected ray and the normal are equal, i.e. ∠i = ∠r

 2492_Laws of reflection.jpg

 

 

((iii) Types of reflection
(a)    Regular Reflection    (b)    Diffused Reflection or Scattering or Diffusion

(a)    Regular Reflection: When the reflection takes place from a perfect plane surface it is called Regular Reflection.  


481_regular reflection.jpg
(b)    Diffused Reflection or Scattering or Diffusion: When the surface is rough light is reflected from the surface from bits of its plane surfaces in irregulardirections. This is called diffusion. This process enables us to see an object from any position.

 89_Irregular reflection.jpg

Characteristics of Reflection by a Plane Mirror
(i)    Distance of object from mirror = Distance of image from the mirror.
(ii)    The line joining the object point with its image is normal to the reflecting surface.
(iii)    The image is laterally inverted (left right inversion).
(iv)    The size of the image is the same as that of the object.
(v)    For a real object the image is virtual and for a virtual object the image is real.
(vi)    The minimum size of a plane mirror, required to see the full self image, is half the size of that person.
(vii)    For a light ray incident at an angle 'i' after reflection angle of deviation d = p -2i 

(viii)    If i = 0 then r = 0, this implies that a ray of light incident normally on a mirror retraces its path.
(ix)    The eye always observes an object in the direction in which the rays enter the eye
(x)    The laws of reflection holds good for all kinds of reflection.
(xi)    Image of an object is the point at which rays after reflection (or reflection) actually converge or appear to diverge from that point.
(xii)    If the direction of the incident ray is kept constant and the mirror is rotated through an angle θ about an axis in the plane mirror then the reflected ray rotates through an angle 2 
θ.
(xiii)    If an object moves towards (or away from) a plane mirror at a speed v, the image will also approach (or recede) at the same speed.
    Further the relative speed of image to the object will be v – (–v) = 2v.

618_two perpendicular mirrors.jpg(xiv)    If two plane mirror are inclined to each other at 90o, the emergent ray is always antiparallel to incident ray, if reflected from each mirror, irrespective of angle of incident.
 


(xv)    When two plane mirror, inclined to each other at an angle θ, the number of images formed can be determined as follows:
    (a)    If  (360/θ) is an even integer, say ‘p’, then number of image formed say q = p – 1, for all position.
    (b)    If (360/θ)  is an odd integer say ‘q’ then number of image formed say p = q, if the object is not on the bisector of the angle between mirrors. Also, p = q – 1, if the object is on the bisector.
    (c)    If  (360/θ) is a fraction, then the number of image formed will be equal to its integral part.
(xvi)    The images are laterally inverted.
(xvii)    The linear magnification is unity.


Illustration 1:     A ray of light on a plane mirror along a vector i+j+k. The normal on incident point is along i+j . Find a unit vector along the reflected ray? 
Solution:     Reflection of a ray of light is just like an elastic collision of a ball with a horizontal ground. Component of incident ray along the inside normal gets reversed while the component perpendicular to it remains unchanged. Thus the component of incident ray vector  A = i+j+k parallel to normal, i.e i+j,  gets reversed while perpendicular to it, i.e. -k  remains unchanged. Thus, the reflected ray can be written as 

             R = -i -j -k
     A unit vector along the reflected ray will be 

 

             r = R/ |R| = (-i -j -k)/√3

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