Title SP-5_Ch-25_Wave Optics.pdf ✅

Chapter Contents Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Introduction Models of Light Huygens’ Principle The Doppler’s Effect Coherent and Incoherent Sources of Light Interference of Light Wave and Young’s Double Slit Experiment Shape of Fringes on Screen Diffraction Resolving Power of Optical Instruments The Validity of Ray Optics Polarisation Introduction By now, you are well versed with laws that govern the formation of images through lens, mirrors and various optical instruments. All what you have read was based on the fact that light travels in a straight line. But from this chapter you will get to know that light does not always travel in straight line, indeed light is a wave. It interferes, it diffracts and it even undergo polarization. This new branch of Physics that deals with the wave nature of light is called “Wave Optics”. MODELS OF LIGHT 1. Corpuscular model : According to this model a luminous body emits a stream of particles in all directions. The particles are assumed to be very-very tiny. It explained the laws of reflection and refraction of light at an interface using concepts of elastic collisions and momentum conservation. Although this law could explain reflection and refraction, this law could not satisfactorily explain phenomenon like interference, polarization and diffraction. 2. Wave model : The wave theory of light was first put forward by Christian Huygen in 1678. On the basis of his wave theory. Huygen explained satisfactorily the phenomenon of reflection, refraction and total internal reflection. This model actually got acceptance when Thomas Young performed his famous interference experiments in 1801. Following Young’s experiments many experiments were carried out involving the interference and diffraction of light waves, these experiments could only be satisfactorily explained by assuming a wave model of light. The only phenomenon that wave theory failed to explain at that time was propagation of light in vacuum, as it was a firm belief that no wave could travel without a medium. Maxwell had developed a set of equations describing the laws of electricity and magnetism and using these equations he derived what is known as the wave equation of electromagnetic waves. From these equations Maxwell calculated theoretically the speed of electromagnetic waves as 0 0 1 c    . Chapter 25 Wave Optics
2 Wave Optics NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 According to Maxwell, light consists of varying electric and magnetic field given as E = E0cos(t – kx) B = B0cos(t – kx) These electric and magnetic fields are normal to each other and also normal to the propagation of light waves. E B y x z HUYGENS’ PRINCIPLE Huygens’ theory is essentially based on a geometrical construction which allows us to determine the shape of the wavefront at any time, if the shape of the wavefront at an earlier time is known. A wavefront is the locus of the points which are in same phase; light ray Spherical wavefronts of a point source The speed with which the wavefronts moves outwards from the source is called the speed of the wave. The energy is carried in the direction perpendicular to the wavefront. At large distances from the source, a small portion of the sphere can be considered as a plane and we have, what is known as a plane wavefront. Plane wavefronts from distant source Light Rays If we know the shape of the wavefront at t = 0, then Huygens’ principle allows us to determine the shape of the wavefront at a later time . Thus, in a way Huygens' principle is based on a geometrical construction which allows us to determine the shape of the wavefront at any time, if the shape of the wavefront at an earlier time is known. According to Huygens’ principle, each point of a wavefront is a source of secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of wave. The envelope of these wavelets gives the shape of the new wavefront called secondary wavefront. Shapes of wavefronts in different situations 1. Reflection from plane mirror Incident wavefront (plane) Reflected wavefront (plane)
NEET Wave Optics 3 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 2. Reflection from curved mirror Reflected wavefront (spherical) Incident wavefront (plane) Reflected wavefront (spherical) Incident wavefront (plane) Reflection from concave mirror Reflection from convex mirror 3. Refraction from plane surface Refracted wavefront (plane) Incident wavefront (plane) Medium-1 Medium-2 4. Refraction through prism (Monochromatic beam) Incident wavefront (plane) Emergent wavefront (plane) 5. Refraction through lens Incident wavefront (plane) Emergent wavefront (spherical) Incident wavefront (plane) Emergent wavefront (spherical) Refraction through convex lens Refraction through concave lens
4 Wave Optics NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Application of Huygens’ Principle to Study Refraction and Reflection 1. Refraction of a Plane Wave: With the help of Huygens' Principle we can derive Snell’s law. Refraction from Rarer to Denser Medium : Let v1 and v2 (v1 > v2) represents the speed of light in medium- 1 and medium-2 respectively. Consider a plane wavefront PQ propagating in the direction PP, incident on the medium boundary at point P at an angle of incidence i. Let t be the time taken to travel from Q to B. Medium 1 Medium 2 Refracted ray r r i i Q B R P A A Incident ray Incident wavefront Refracted wavefront P v t2 v t 1  QB = v1t From the point P, draw a sphere of radius v2t, let BR represent the forward tangent plane. It is refracted wavefront at t.  PR = v2t From PQB, 1 1 sin sin QB vt vt i PB PB PB i     ...(i) Also from PRB, 2 2 sin sin PR vt vt r PB PB PB r     ...(ii) Equating (i) and (ii), we have 1 2 1 2 sin sin sin sin vt v t v i i r rv    ...(iii) This prediction is opposite to the prediction as per the Newton’s Corpuscular Theory. Also, if 1 be the refractive index of light in medium 1, then 1 1 1 1 c c v v      Similarly, 2 2 2 2 and c c v v    Hence, from eq. (iii), 1 2 2 1 sin sin i v r v     QB = n vt  1 1 and PR = n vt   2 2 On dividing, we have  11 2 22 1 sin sin v i v r       The frequency of the wave does not change as it travels from one medium to another as the frequency is source dependent.