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When two or more than two waves superimpose over each other at a common particle of the medium then the resultant displacement (y) of the particle is equal to the vector sum of the displacements (\[{{y}_{1}}\] and \[{{y}_{2}}\]) produced by individual waves. i.e. \[\overrightarrow{y\,}={{\overrightarrow{\,y}}_{1}}+{{\overrightarrow{\,y}}_{2}}\]

Reflection \[BC=AD\] and \[\angle i=\angle r\]   Refraction \[\frac{BC}{AD}=\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{\sin i}{\sin r}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}\]      

(1) Suggested by Huygens (2) The locus of all particles in a medium, vibrating in the same phase is called Wave Front (WF) (3) The direction of propagation of light (ray of light) is perpendicular to the WF.              (4) Every point on the given wave front acts as a source of new disturbance called secondary wavelets which travel in all directions with the velocity of light in the medium. (5) A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new wave front at that instant. This is called secondary wave front Different types of wavefront

Type of wavefront	Intensity	Amplitude
Spherical	\[I\propto \frac{1}{{{r}^{2}}}\]	\[A\propto \frac{1}{r}\]
Cylindrical	\[I\propto \frac{1}{r}\]	\[A\propto \frac{1}{\sqrt{r}}\]
Plane	\[I\propto {{r}^{0}}\]	\[A\propto {{r}^{0}}\]

 

(1) Wave theory of light was given by Christian Huygen. According to this, a luminous body is a source of disturbance in a hypothetical medium ether. This medium pervades all space. (2) It is assumed to be transparent and having zero inertia. The disturbance from the source is propagated in the form of waves through the space. (3) The waves carry energy and momentum. Huygen assumed that the waves were longitudinal. Further when polarization was discovered, then to explain it, light waves were, assumed to be transverse in nature by Fresnel. (4) This theory explains successfully, the phenomenon of interference and diffraction apart from other properties of light. (5) The Huygen's theory fails to explain photo-electric effect, Compton's effect etc. (6) The wave theory introduces the concept of wavefront.  

(1) Newton thought that light is made up of tiny, light and elastic particles called corpuscles which are emitted by a luminous body. (2) The corpuscles travel with speed equal to the speed of light in all directions in straight lines. (3) The corpuscles carry energy with them. When they strike retina of the eye, they produce sensation of vision. (4) The corpuscles of different colour are of different sizes (red corpuscles larger than blue corpuscles). (5) The corpuscular theory explains that light carry energy and momentum, light travels in a straight line, Propagation of light in vacuum, Laws of reflection and refraction (6) The corpuscular theory fails to explain interference, diffraction and polarization. (7) A major prediction of the corpuscular theory is that the speed of light in a denser medium is more than the speed of light in a rarer medium. The truth is that the speed of the light is smaller in a denser medium. Therefore, the Newton's corpuscular theory is wrong.

The branch of optics that deals with the study and measurement of the light energy is called photometry. (1) Radiant flux (R) : The total energy radiated by a source per second is called radiant flux. It's S.I. unit is Watt (W). (2) Luminous flux \[(\phi )\] : The total light energy emitted by a source per second is called luminous flux. It represents the total brightness producing capacity of the source. It's S.I. unit is Lumen (lm). (3) Luminous efficiency \[(\eta )\] : The Ratio of luminous flux and radiant flux is called luminous efficiency i.e. \[\eta =\frac{\varphi }{R}\]. Luminous flux and efficiency

Light source	Flux (lumen)	Efficiency (lumen/watt)
40 W tungsten bulb 60 W tungsten bulb 500 W tungsten bulb 30 W fluorescent tube	465 835 9950 1500	12 14 20 50

(4) Luminous Intensity (L) : In a given direction it is defined as luminous flux per unit solid angle i.e. \[L=\frac{\varphi }{\omega }\to \frac{\text{Light energy}}{\sec \,\times \text{solid angle }}\xrightarrow{\text{S}\text{.I}\text{. unit}}\frac{\text{lumen}}{\text{steradian}}=\text{candela}\,\text{(}Cd\text{)}\] The luminous intensity of a point source is given by : \[L=\frac{\varphi }{4\pi }\]\[\Rightarrow \]\[\varphi =4\pi \times (L)\] (5) Illuminance or intensity of illumination (I) : The luminous flux incident per unit area of a surface is called illuminance.  \[I=\frac{\varphi }{A}\]. It's S.I. unit is \[\frac{\text{Lumen}}{{{m}^{\text{2}}}}\] or Lux (ix) and it's C.G.S. unit is Phot.   \[1\,\text{Phot}={{10}^{4}}\text{Lux}=\frac{\text{1}\,\text{Lumen}}{c{{m}^{\text{2}}}}\] (i) Intensity of illumination at a distance r from a point source is  \[I=\frac{\varphi }{4\pi {{r}^{2}}}\Rightarrow I\propto \frac{1}{{{r}^{2}}}\]. (ii) Intensity of illumination at a distance r from a line source is \[I=\frac{\varphi }{2\pi rl}\Rightarrow I\propto \frac{1}{r}\] (iii) In case of a parallel beam of light \[I\propto {{r}^{0}}\]. (iv) The illuminance represents the luminous flux incident on unit area of the surface, while luminance represents the luminous flux reflected from a unit area of the surface. (6) Relation Between Luminous Intensity (L) and Illuminance (I) : If S is a unidirectional point source of light of luminous intensity L and there is a surface at a distance r from source, on which light is falling normally. (i) more...

(1) Microscope : In reference to a microscope, the minimum distance between two lines at which they are just distinct is called Resolving limit (RL) and it?s reciprocal is called Resolving power (RP) \[R.L.=\frac{\lambda }{2\mu \sin \theta }\] and\[R.P.=\frac{2\mu \sin \theta }{\lambda }\Rightarrow \]\[R.P.\propto \frac{1}{\lambda }\] \[\lambda =\] Wavelength of light used to illuminate the object, \[\mu =\] Refractive index of the medium between object and objective, \[\theta =\] Half angle of the cone of light from the point object, \[\mu \sin \theta \]= Numerical aperture. (2) Telescope : Smallest angular separations \[(d\theta )\] between two distant objects, whose images are separated in the telescope is called resolving limit. So resolving limit \[d\theta =\frac{1.22\lambda }{a}\] and  resolving power \[(RP)=\frac{1}{d\theta }=\frac{a}{1.22\lambda }\Rightarrow \]\[R.P.\propto \frac{1}{\lambda }\] where a = aperture of objective.

If two telescopes are mounted parallel to each other so that an object can be seen by both the eyes simultaneously, the arrangement is called 'binocular'. In a binocular, the length of each tube is reduced by using a set of totally reflecting prisms which provide intense, erect image free from lateral inversion. Through a binocular we get two images of the same object from different angles at same time. Their superposition gives the perception of depth along with length and breadth, i.e., binocular vision gives proper three-dimensional (3D) image.

Reflecting telescopes are based upon the same principle except that the formation of images takes place by reflection instead of by refraction. If \[{{f}_{o}}\] is focal length of the concave spherical mirror used as objective and \[{{f}_{e}},\] the focal length of the eye-piece, the magnifying power of the reflecting telescope is given by \[m=\frac{{{f}_{o}}}{{{f}_{e}}}\] Further, if D is diameter of the objective and d, the diameter of the pupil of the eye, then brightness ratio \[(\beta )\] is given by \[\beta =\frac{{{D}^{2}}}{{{d}^{2}}}\]

It is also type of terrestrial telescope but of much smaller field of view. (1) Objective is a converging lens while eye lens is diverging lens. (2) Magnification : \[{{m}_{D}}=\frac{{{f}_{0}}}{{{f}_{e}}}\left( 1-\frac{{{f}_{e}}}{D} \right)\] and \[{{m}_{\infty }}=\frac{{{f}_{0}}}{{{f}_{e}}}\] (3) Length : \[{{L}_{D}}={{f}_{0}}-{{u}_{e}}\] and \[{{L}_{\infty }}={{f}_{0}}-{{f}_{e}}\]