Sharjah Indian School, Sharjah Boys Wing

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1 NOTES ON Optics (Class 12-Boys Wing) Page 01 Optics deals with the study of light. Light is a form of energy that makes the things visible. There are different theories of light such as, Corpuscular theory, wave theory and photon theory etc. The path of light is called a ray of light, and a bundle of such rays constitutes a beam of light. Reflection Laws of reflection (i) The angle of reflection (i.e., the angle between reflected ray and the normal to the reflecting surface or the mirror) equals the angle of incidence (angle between incident ray andthe normal). (ii) the incident ray, reflected ray and the normal to the reflecting surface at the point of incidence lie in the same plane. Sign Convention The sign convention used in the measurement of different distances is illustrated in the following diagram. Relation between focal length and radius of curvature of a spherical mirror. Let R be the radius of curvature and f, the focal length of a spherical mirror as shown. Consider a ray of light incident on the surface of the mirror at an angle of incidence θ. We know, angle = arc/radius (1) (2) Dividing (2)/(1), we get or R = 2f

2 NOTES ON Optics (Class 12-Boys Wing) Page 02 The mirror Equation Law of distances 1. Concave mirror Consider an object placed beyond C of a concave mirror so that a real, diminished image Is formed as shown: In triangles ABP and A B P, In triangles MPF and B A F But MP = AB. Hence (1) = (2) or Cross multiplying, uv uf = vf. Dividing throughout by uvf, we get By applying sign convention, f, u and v are negative. 2. Convex mirror. A convex mirror always forms diminished virtual images, irrespective of the position of the object as shown below. [Try yourself to derive the mirror equation using the same method as given above] MAGNIFICATION (m) Linear magnification (m) is the ratio of the height of the image (h i ) to the height of the object (h o ). get, Using the triangles A B P and ABP in the above diagram and applying sign convention, we = -

3 REFRACTION page3 It is the phenomenon of bending of light when it enters from one medium to another having different optical densities. The deviation occurs at the surface of separation due to the sudden change in speed of light. Laws of refraction (i) The incident ray, the refracted ray and the normal at the point of incidence, all lie in the same plane. (ii) Snell s Law:- The ratio of the sine of the angle of incidence to the sine of angle of refraction is a constant for a given pair of media and for a given colour of light. This constant is called the refractive index of the second medium with respect to the first (n 21). i.e. n 21 = [The refractive index of a medium with respect to air is called its absolute refractive index and that with respect to another medium is called relative refractive index.] Qn. Show that for a parallel sided glass slab, the incident and emergent rays are parallel to each other. Consider a ray passing through a rectangular glass slab of refractive index n g, as shown beside. By Snell s law, In the first refraction, n g = (1) In the second refraction, n g = (2) Hence = But r 1 = i 2,being alternate interior angles. Thus we get sin i 1 = sin r 2 or i 1 = r 2. Thus, the incident and emergent rays are parallel to each other. Qn. Show that relative refractive index is the ratio of the absolute refractive indices of the media. Consider two media of absolute refractive indices n 1 and n 2 through which a light ray from air gets refracted as shown: By Snell s law on first refraction, i 1 n 1 = r 1 r 2 n 1 r 3 r 4 n 2 e on second refraction, n 21 = on 3 rd refraction n 2 =

4 = page4 But being alt. int. angles, r 1 = r 2 and r 3 = r 4. Further, i = e (parallel sided slab) Hence, i.e,.. Show that the refractive index of a medium is the ratio of the real depth and apparent depths.] Let O be an object placed at the bottom of medium of refractive index n. Its image is appeared to be formed at I as shown in the figure. From the figure, Sin i = NM/ OM and sin r = NM/IM By Snell s law, the refractive index, n = Thus, n = As the points M and N are close, OM ON & IM IN So, n = i.e. Refractive index = Note: The shift of the image when a glass slab of thickness t is kept on a surface can be calculated as follows: Shift (s) = ON IN = ON ON/n = ON (1 1/n) i.e. Shift (s) = t (1-1/n) Application of refraction:- (i) Twinkling of stars (ii) Swimming pool appears to be shallower than it really is. (iii) Delay in sunset and early sunrise due to atmospheric refraction. (By this, the duration of day increases by 4min.) - Refer page 318 of the text book. TOTAL INTERNAL REFLECTION When a ray travels from denser to a rarer medium, the angle of refraction increases with the angle of incidence. At given angle of incidence, called the critical angle (i c ), the refracted ray grazes through the surface of separation of the two media i.e. r = 90 o. But when the angle of incidence exceeds this, the ray gets totally and internally reflected. This phenomenon is called total internal relection. r r = 90 o Rarer i i c i > i c Denser (i) n = i.e. Hence the conditions for T.I.R are:- (i) The light should pass from denser to a rarer medium. (ii) The angle of incidence should be greater than the critical angle of the medium

5 NOTES ON Optics (Class 12-Boys Wing) Page 05 Applications of T.I.R (i) Total reflecting prisms:- These are the right angled isosceles prisms having critical angle less than 45 o. They are used to turn a ray through 90 o (as used in periscopes) and to turn a ray through 180 o (as used in bicycle reflectors and to make an inverted image erect. (Refer the figures given) (ii) Optical fibres:- These are the devices used for transmitting audio and video signals through long distances. They are fabricated with high quality composite glass/quartz fibres. Each fibre consists of a core of high refractive index and a cladding layer of low refractive index. The signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end without any appreciable loss in the intensity. As the fibre is very thin and refractive index of the core is very high, the angles of incidence always exceeds critical angle. This ensures continuous T.I.R. Optical fibre bundles are used as light pipes to facilitate visual examination of internal organs like esophagus, stomach and intestines. They are also used as decorative lamps. (iii) Mirage and (iv) Diamonds (Refer pages 321 and 322)