Content text 4. Light Refraction.pdf
4 CHAPTER CONTENTS Refraction of Light Law of refraction of light Refractive index Refraction through glass slab Spherical lens Rules for image formation by ray diagram method Image formation by lens Numerical method in lens Total internal reflection Real & apparent depth & height ➢ REFRACTION OF LIGHT DEFINITION : When light rays travelling in a medium are incident on a transparent surface of another medium they are bent as they travel in second medium. N1 Normal N2 Incident ray Refracted ray Q r i Plane transparent surface P R X Y Rarer Denser Fig. Refraction of light from a plane transparent denser surface. SOME ASSOCIATED TERMS ◆ Transparent surface : The plane surface which refracts light, is called transparent surface. In diagram, XY is the section of a plane transparent surface. ◆ Point of incidence : The point on transparent surface, where the ray of light meets it, is called point of incidence. In diagram, Q is the point of incidence. ◆ Normal : Perpendicular drawn on the transparent surface at the point of incidence, is called normal. In diagram, N1QN2 is the normal on surface XY. ◆ Incident ray : The ray of light which strikes the transparent surface at the point of incidence, is called incident ray in diagram PQ is the incident ray. ◆ Refracted ray : The ray of light which travels from the point of incidence into the other medium, is called refracted ray. In diagram, QR is the refracted ray. ◆ Angle of incidence : The angle between the incident ray and the normal on the transparent surface at the point of incidence, is called the angle of incidence. It is represented by the symbol i. In diagram, angle PQN1 is the angle of incidence. ◆ Angle of refraction : The angle between the refracted ray and the normal on the transparent surface at the point of incidence, is called angle of refraction. It is represented by symbol r. In diagram angle RQN2 is the angle of refraction. ◆ Plane of incidence : The plane containing the normal and the incident ray, is called plane of incidence. For the diagram, plane of book page is the plane of incidence. LIGHT : REFRACTION
◆ Plane of refraction : The plane containing the normal and the refracted ray, is called plane of refraction. For the diagram, plane of book page is the plane of refraction. ➢ LAW OF REFRACTION OF LIGHT ◆ First Law : The incident ray, the normal to the transparent surface at the point of incidence and the refracted ray, all lie in one and the same plane. ◆ Second Law : The ratio of sine of angle of incidence to the sine of the angle of refraction is constant and is called refractive index of the second medium with respect to the first medium. sin r sin i = μ ➢ REFRACTIVE INDEX (a) Refractive Index in terms of Speed of Light: The refractive index of a medium may be defined in terms of the speed of light as follows : Refractive index = Speed of light in medium Speed of light in vacuum or μ = v c (b) Refractive Index in terms of Wavelength : Since the frequency () remains unchanged when light passes from one medium to another, therefore, μ = v c = med vac = med vac (c) Relative Refractive Index : The relative refractive index of medium 2 with respect to medium 1 is defined as the ratio of speed of light (v1) in the medium 1 to the speed of light (v2) in medium 2 and is denoted by 1μ2. Thus, 1μ2 = 2 1 v v = 2 1 = 1 2 As refractive index is the ratio of two similar physical quantities, so it has no unit and dimension. FACTORS ON WHICH THE REFRACTIVE INDEX OF A MEDIUM DEPENDS ARE : (i) Nature of the medium. (ii) Wavelength of the light used. (iii) Temperature (iv) Nature of the surrounding medium. It may be noted that refractive index is a characteristic of the pair of the media and also depends on the wavelength of light, but is independent of the angle of incidence. ➢ REFRACTION THROUGH GLASS SLAB (a) Refraction through a rectangular glass slab and principle of reversibility of light : Consider a rectangular glass slab, as shown in figure. A ray AE is incident on the face PQ at an angle of incidence i. On entering the glass slab, it bends towards normal and travels along EF at an angle of refraction r. The refracted ray EF is incident on face SR at an angle of incidence r'. The emerged ray FD bends away from the normal at an angle of refraction e. Thus the emergent ray FD is parallel to the incident rays AE, but it has been laterally displaced with respect to the incident ray. There is shift in the path of light on emerging from a refracting medium with parallel faces. Lateral shift : Lateral shift is the perpendicular distance between the incident and emergent rays when light is incident obliquely on a refracting slab with parallel faces. Factors on which lateral shift depends are : (i) Lateral shift is directly proportional to the thickness of glass slab. (ii) Lateral shift is directly proportional to the incident angle. (iii) Lateral shift is directly proportional to the refractive index of glass slab. (iv) Lateral shift is inversely proportional to the wavelength of incident light. N1 Glass air N2 A B Incident ray P S Q R μa μg t→Thickness i r E Refracted ray air, a r' F N1 N2 e c d Lateral displacement Emergent ray D Proof for i = e Case-I :
For light going from air to glass at point E. μa sin i = μg sin r ..... (1) Case-II : For light going from glass to air at point F. μg sin r = μa sin e .....(2) From (1) & (2) we can say that i = e incident & emergent rays are parallel to each other. ➢ SPHERICAL LENS ◆ Definition : A piece of a transparent medium bounded by at least one spherical surface, is called a spherical lens. ◆ Types : There are two types of spherical lenses: (i) Convex or Converging Lenses : These are thick in the middle and thin at the edges. (a) (b) (c) Fig. Three types of convex lenses (a) Double Convex Lens : It has both the surfaces convex. (b) Plano–Convex Lens : It has one surface plane and the other surface convex. (c) Concavo–Convex Lens : It has one surface concave and the other surface convex. (ii) Concave or Diverging Lenses : These are thin in the middle and thick at the edges. There are three types of concave lenses : (a) (b) (c) Fig. Three types of concave lenses (a) Double Concave Lens : It has both the surfaces concave. (Fig.) (b) Plano–Concave Lens : It has one surface plane and the other surface concave. (fig.) (c) Convexo–Concave Lens : It has one surface convex and the other surface concave. (fig.) SOME ASSOCIATED TERMS : (i) Centre of curvature (C) : The centre of curvature of the surface of a lens is the centre of the sphere of which it forms a part, because a lens has two surfaces, so it has two centres of curvature. In figure (a) and (b) points, C1 and C2 are the centres of curvature. (ii) Radius of curvature (R) : The radius of curvature of the surface of a lens is the radius of the sphere of which the surface forms a part. R1 and R2 in the figure (a) and (b) represents radius of curvature. (iii) Principal axis (C1C2) : It is the line passing through the two centres of curvature (C1 and C2) of the lens. Optical Centre Radius of Centre of Curvature Curvature R1 R2 C2 O C1 P1 Principal axis P2 (a) (b) Optical Centre P1 O P2 Centre of Curvature R1 C1 Radius of Curvature C2 Principal axis R2 Figure : Characteristics of convex and concave lenses (iv) Optical centre : If a ray of light is incident on a lens such that after refraction through the lens the emergent ray is parallel to the incident ray, then the point at which the refracted ray intersects, the principal axis is called the optical centre of the lens. 2 1 OP OP = 2 2 1 1 P C P C = 2 1 R R If the radii of curvature of the two surfaces are equal, then the optical centre coincides with the geometric centre of the lens.
A R2 C2 C1 P1 P2 (a) O B R1 (b) O (c) O (v) Principal foci and focal length : (A) First principal focus and first focal length : It is a fixed point on the principal axis such that rays starting from this point (in convex lens) or appearing to go towards this point (concave lens), after refraction through the lens, become parallel to the principal axis. It is represented by F1. F1 O f O F1 f Figure : Ray diagram showing first principal focus (B) Second principal focus and second focal length : It is a fixed point on the principal axis such that the light rays incident parallel to the principal axis, after refraction through the lens, either converge to this point (in convex lens) or appear to diverge from this point (in concave lens). It is denoted by F2. O F2 f F2 O f Figure : Ray diagram showing second principal focus If the medium on both sides of a lens is same, then the numerical values of the first and second focal lengths are equal. Thus f = f (vi) Aperture : It is the diameter of the circular boundary of the lens.
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