Light notes

Introduction of light :-

  • We see different colourful objects throughout the day but in a dark room or in night our vision and capacity to distinguish colours diminishes.  
  • We use a bulb then in the light of the bulb we can see even in dark room or in night. 
  • Sun is our source of light on earth. 
  • When light falls on an object then the object absorbs a few of the colours of light and reflects the rest of the colours. When this reflected light from object reaches our eyes then an image is formed on retina and we can see the object and its colour. 
  • An object appears red when it reflects red colour from the light falling on it. 
  • If an object transmits all colours through it then we see it as transparent. 
  • When object absorbs all colours falling on it then the object appears black. 
  • Similarly when an object reflects all colours falling on it then it will appear white to us. 
  • Light travelling in straight lines.
  • When light rays falls on very small obstacles (of the order of the wave length of the light) then light bends around the edges of the object this phenomenon is known as diffraction. 
  • Scientist de Broglie proposed dual nature of light and said that light behaves both as wave and as particle. 
  • This dual nature is represented as wave packet in quantum mechanics. According to this concept the light photons behave some times as wave and some times as particles.  

Reflection of light :-

Reflection is the change in direction of a wave front at an interface between two different media so that the wave front returns into the medium from it originated. 
We encounter two types of reflections in routine : - regular reflection and diffused reflection. 

Regular reflection :-

The reflection of incident light beam by smooth plane surface in the specific direction in the same medium is known as regular reflection. 
When light is incident on any smooth plane surface (like mirror) then on looking from a specific direction that plane surface looks shinning while from other direction the surface does not shine. 
If we change the plane of the mirror then the mirror shines from some other direction. 
Similarly if the direction of incidence of light is changed then mirror gives shining from some other direction decided by the laws of reflection. 



Diffused Reflection :-

Scattering of light in all directions in the same medium by rough surface is known as diffused reflection.
When light falls on any part of wall from any opening or window then that part of the wall looks bright from every where in the room. This happens because light reflect in all directions after striking the wall. We see almost all objects because of this reason. 
Rough surfaces, dust particles and microscopic smoke particles diffuse the light in different directions. 
When sun-light enters the atmosphere then the air molecules scatter blue light more than they scatter red light and thus day time sky is blue. 
During sunset or sunrise we see red and orange colour because the blue light has been scattered out and away from the line of sight. 
If we look the outer space from outside our atmosphere then we shall see it black.  
Generally, reflecting surface is applied (like silver or aluminium layer) on the back or front of glass or transparent material and then it is used as mirror or reflecting plane. 


Laws of reflection :-

When light rays propagating through medium-strike at the surface of medium and return back in a particular direction in the medium, then this phenomena is known as reflection of light. 
Reflection Mirrors are often used as reflectors and are made by silvering a surface of a glass.
Following are rules of reflection 
(i) Incident ray, reflected ray and perpendicular on point of incidence are in same plane. 
(ii) The angle extended by incident ray with the perpendicular is same as the angle extended by reflected ray with the perpendicular. 
Angle of incidence (∠i) = angle of reflection (∠r)   


Image formation in plane mirror :-

  1. The image formed in a plane mirror is virtual. 
  2. The image is at the same distance from mirror as the distance of object from mirror though both are in opposite directions. 
  3. Size of the image is same as that of object. When we look at our image in a mirror then we observe that our left part is right in the image and vice-versa. This change is known as lateral inversion. 




Prove that image in the mirror is at the same distance from mirror as that of the distance of object from the mirror. 

Solution : MM' is a reflecting surface in figure P  is an object from which rays PO and PO' are incident on MM'. Rays OQ and O'Q' are reflected rays of PO and PO' respectively. Extending these reflected rays construct a virtual image P' of the object P . ON and O'N' are perpendiculars on mirror. 




according to law of refection ∠1 = ∠4 ---(1) 
according to law of refection ∠5 = ∠8 ---(2)
∠4 = ∠9 (vertical opposite angle) ---(3) 
∠5 = ∠10 (vertical opposite angle) ---(4)
then by equation ---(1) & ---(3)
∠1 = ∠4 = ∠9 ---(5)
then by equation ---(2) & ---(4)
∠5 = ∠8 = ∠10 ---(5)
Angles on one side of a straight line always add to 180° degrees so
∠POO' = 180° - ∠1 ---(6)
∠P'OO' = 180° - ∠9 ---(7)
∵ ∠1 = ∠9 
So ∠POO' = ∠P'OO' ---(8)
In triangle POO' and P'OO' 
OO' = OO' {Common base}
∠5 = ∠10 {by equation ---(5)}
∠POO' = ∠P'OO' {by equation ---(8)}
So, by angle side angle rule triangle POO' and P'OO' are similar then
PO = PO' ---(9)
In triangle PO'M' and P'O'M'
M'O' = M'O' {Common base}
∠5 = ∠10 {by equation ---(5)}
PO = PO' {by equation ---(9)}
So, by side angle side rule triangle PO'M' and P'O'M' are similar then
PM' = P'M' (Proved)

Spherical mirror :- 

  • Mirrors having spherical reflecting surfaces are called spherical mirrors.
  • Their surfaces are just like a part of hollow spheres.
  • Images from such surfaces are different in shapes. 
  • Shape and size of the image depends upon the nature of curved surface.   
  • There are two types of spherical mirrors. 

Concave mirror :- 

  • Spherical mirrors whose curved reflecting surface is curved from inside are known as concave mirrors.   
  • Such mirrors are known as front coated mirrors.
  • Such mirrors are known as converging mirror. 

Convex mirror :- 

  • Such spherical surfaces whose outer part is used as mirror surface are known as convex mirrors.
  • These are also back coated convex mirrors.  
  • Such mirrors are known as diverging mirror.




Some important terminology related to mirror :-

Centre of curvature :- 

  • Spherical mirror may be considered as part of a hollow sphere and the Centre of that sphere is known as Centre of curvature.
  • It is denote by 'C'.

Radius of curvature :- 

  • Distance from pole to Centre of curvature is called radius of curvature
  • It is denote by 'c'.

Focal point :- 

  • When parallel ray beam gets reflected from a concave mirror then the reflected rays converge at a point in front of mirror. This point is called focus of a concave mirror. 
  • When parallel rays reflect from a convex mirror then they diverge in such a way that when extended backwards these rays meet at a point behind the mirror. It seems that the reflected rays are originating from this point. This point is called the focus of a convex mirror. 
  • It is denote by 'F'.

Focal length :- 

  • The distance from pole to focus is known as focal length
  • It is denote by 'f'.

Pole :- 

  1. Centre point of the curved surface of mirror is called pole.
  2. It is denote by 'O'.

Principal axis :-  

  • A line joining the pole `P` to Centre of curvature of the mirror, produced on both sides is called principal axis of mirror.      


Cartesian sign convention :- 

In Cartesian sign convention all signs are taken from pole of the mirror, also called as origin point and principal axis is considered as x-axis. Rules are as follows. 
  1. All distances parallel to principal axis are measured from pole or origin point. 
  2. Object is placed left to the mirror and thus the incident rays from object are always from the left. 
  3. All distances parallel to principal axis and towards left side of origin point (along-x axis) are taken as negative. For example the distance of object in a convex as well as concave mirror is always negative. 
  4. Similarly all distances towards right side of the origin point (along + x axis) are taken as positive. 
  5. Heights measured above the principal axis are taken as positive (along + y axis).
  6. Heights measured below the principal axis (along - y axis) are taken as negative. 

Cartesian sign convention for concave mirror :-

  • According to Cartesian sign convention the object distance, focal length and radius of curvature are always negative in concave minor. 
  • When image is formed towards left of the origin in a concave mirror then its distance will be taken as negative while the distance will be positive for images formed towards right side of a concave mirror. 
  • When image is upright then its height will be taken as positive and when image is below the principal axis and downwards then its height is taken as negative. 


Cartesian sign convention for convex mirror :-

  • For a convex minor the object distance will be negative as per the sign convention. 
  • In convex mirror the focal length and radius of curvature are always towards the right side of the origin point and hence focal length and radius of curvature are always taken positive in a convex mirror. 
  • In convex mirror the image is always towards right side of the pole and hence image distance is always positive. 
  • Similarly the image is always upright and thus height of image is always positive in this case. 

Prove that radius of curvature is double of the focal length for a small aperture concave mirror. 

Solution :- 
Reflection from a concave minor is shown in the figure.
Rules of reflection of plane mirror also applies to spherical mirror. 
In the figure AP is incident ray that is parallel to principal axis and after reflecting from concave minor goes in PQ direction. It passes through point F on the principal axis. 
Line CP is perpendicular to mirror at point P and hence CP is the radius of curvature of this concave minor. 
      ∠APC = ∠QPC --- (1) From the laws of reflection
 ∠APC = ∠PCF --- (2) (Alternate angels) 
∠PCF = ∠QPC = ∠APC --- (3)
Therefore in triangle PCF, 
PF = FC --- (4)
When aperture is small then point P will be near to the pole 
PF = OF --- (5) 
By equation --- (4) & (5)
PF = FC = OF --- (6) 
OC = OF + FC
or
OC = OF + OF
or
OC = 2OF
R = 2f 

Image formation in spherical mirror :-

When focal length and radius of curvature of a convex or concave mirror is known then position of image of any object can be ascertained. 
At least two reflected rays should intersect to get the image. Generally we use specific incident rays to get the position of image in both the concave and convex minors. 

Concave mirror :-

  • Incident rays AL parallel to principal axis of a concave mirror gets reflected from point L of minor and passes through focus in the A' direction 

  • A ray BM passing through focus of a concave mirror gets reflected from the mirror and becomes parallel to principal axis in MB' direction. 
Ray that passes through radius of curvature in concave mirror get reflected in the same direction from which they are arrived. The reason is that any line joining any point of mirror to the Centre of curvature is a perpendicular on that point and hence angle of incidence and angle of reflection in such case is zero.



 All rays that are obliquely incident on a concave minor will reflect in another oblique direction as per the rules of reflection. 

Convex mirror :-

In a convex mirror the ray AL diverges after reflection and when extended backwards the reflected ray AL' meets at focus. It seems as if the ray is diverging from focus.


In a convex mirror a ray towards focus strike the mirror at M and gets reflected in MB' direction parallel to principal axis.


All rays that are obliquely incident on a convex minor will reflect in another oblique direction as per the rules of reflection. 


Ray that approaches towards Centre of curvature in convex mirror get reflected in the same direction from which they are arrived.