Title WAVE OPTICS.pdf ✅

 Digital www.allendigital.in [ 125 ] Introduction • The Greeks believed that light consisted of tiny particles (corpuscles) that were emitted by a light source and these particles stimulated the perception of vision upon striking the observer’s eye. Newton used this particle theory to explain the reflection and refraction (bending) of light. Newton's Corpuscular Theory ➢ Light consists of little, invisible particles known as corpuscles. ➢ These are constantly emitted by all luminous light sources in all directions. ➢ When corpuscles strike the retina of our eye then they produce the sensation of vision. ➢ These corpuscles travel with the velocity of light in straight lines. ➢ Their velocity changes with the change of medium. ➢ The different colors of light are due to different size of these corpuscles. ➢ The rest mass of these corpuscles is zero. The phenomena explained by this theory (i) Reflection (ii) Refraction (iii) Rectilinear propagation of light. The phenomena not explained by this theory (i) Interference (ii) Diffraction (iii) Polarisation (iv) Photoelectric effect Note: Newton proposed in his theory that light travels faster in denser medium than in rarer medium but he was proved wrong later. Wave front and Huygens’ Principle In 1678, one of Newton’s contemporaries, the Dutch scientist Christian Huygens, was able to explain many other properties of light by proposing that light is a wave. Huygens showed that a wave theory of light could also explain reflection and refraction. Huygens' Wave theory of light ➢ The locus of all particles vibrating in same phase is known as wavefront. ➢ Light travels in a medium in the form of wavefront. ➢ When light travels in a medium then the particles of medium start vibrating and consequently a disturbance is created in the medium. ➢ Every point on the wavefront becomes the source of secondary wavelets. It emits secondary wavelets in all directions which travel with the speed of light. Corpuscles 02 Wave Optics
NEET : Physics [ 126 ] www.allendigital.in  Digital ➢ The tangent plane to these secondary wavelets represents the new position of wavefront. The phenomena explained by this theory ➢ Reflection, Refraction, interference and diffraction ➢ Rectilinear propagation of light. ➢ Velocity of light in rarer medium being greater than that in denser medium. The phenomena not explained by this theory (1) Photoelectric effect (2) Polarisation Note: Huygens considered that the environment is filled with anisotropic luminiferous ether but later he was proved wrong, later. Reflection and Refraction of plane waves at a plane surface using wave fronts Types of Wavefront: The shape of wavefront depends upon the shape of the light source from which the wavefront originates. On this basis there are three types of wavefronts. (1) Spherical Wavefront (2) Cylindrical Wavefront (3) Plane Wavefront (1) Spherical Wavefront → Spherical wavefront originates from point source. → 1 Intensity (I) Area  2 2 1 I (Area 4 r ) r   =  → Intensity  (Amplitude)2  2 2 1 A r  1 A r   (2) Cylindrical Wavefront → Cylindrical wavefront originates from linear source. → 1 Intensity (I) Area   1 I (Area 2 rh) r  =  → Intensity  (Amplitude)2  1 2 A r  1 A r   Secondary source Common tangent source source Wavefront Secondary Wavelets Secondary Wavefront Primary Wavefront
Wave Optics  Digital www.allendigital.in [ 127 ] (3) Plane Wavefront → Plane wavefront originates from the source situated at very large distance. → 1 Intensity (I) Area  I = constant (Area is constant) → Intensity  (Amplitude)2 A = constant Summary Sr. No. Wavefront Shape of Light Source Diagram or shape of wavefront Variation of amplitude (A) with distance Variation of Intensity (I) with distance 1. Spherical Point source 1 A r  2 1 I r  2. Cylindrical Linear source/ Slit 1 A r  1 I r  3. Plane Extended Large source / Point source at very large distance A: constant A ∝ r o I: constant I ∝ r o Illustration 1: If amplitude of light at 10 m from a small light bulb is A0 then find amplitude of light at a distance 50 m from the same light bulb? Solution: 1 A r   1 2 o 2 1 2 A r A 50 A r A 10 =  =  o 2 A A 5 = Law of reflection by huygen’s wave theory BB' v t = 1  AA' v t = 1 AA' BB' =  In ABB' BB' sini AB' = ...(i) In B'A'AAA' sinr AB' = ...(ii) Divide (i) by (ii) sini BB' 1 sinr AA' = =  sin i sin r =  i r =
NEET : Physics [ 128 ] www.allendigital.in  Digital Law of refraction by huygen’s wave theory BB' v t = 1 AA' v t = 2 In ABB’ BB' sini AB' = ...(i) In AA’B’ AA' sinr AB' = ...(ii) Divide (i) by (ii) sini BB' sinr AA' = 1 1 2 2 2 1 sini v t v sinr v t v  = = =  1 2  = sini sinr Illustration 2: A plane wavefront is incident on given optical device in each case. Draw the correct wavefront after interaction of light ray with the Optical device. Solution: Illustration 3: A plane wavefront of monochromatic light is incident on given optical device. Draw the correct wavefront after interaction of light ray with the Optical device. Solution: Spherical wavefront Spherical wavefront Plane wavefront