REFLECTION OF LIGHT The laws o relection are.. (i) The incident ray, relected ray and the normal to the relecting surace at the point o incidence lie in the same plane (ii) The angle o relection (i.e., the angle between relected ray and the normal to the relecting surace or the mirror) equals the angle o incidence (angle between incident ray and the normal). Relation between ocal length and radius o curvature o a mirror & Mirror ormula R 2 + m I v u v O u According to the new sign convention, v u (i) All distances are measured rom the pole o the mirror or the optical centre o the lens. (ii)the distances measured in the same direction as the incident light are taken as positive and those measured in the direction opposite to the direction o incident light are taken as negative. (iii) The heights measured upwards with respect to x-axis and normal to the principal axis (x-axis) o the mirror/lens are taken as positive and measured downwards are taken as negative.
Reraction - When a ray o light enters rom one transparent medium into another, there is a change in speed and direction o the ray in the second medium. This phenomenon is called reraction. Laws o Reraction : (i) The incident ray, the reracted ray and the normal to the surace separating the two media, all lie in the same plane. (ii) Snell s Law : For two media, the ratio o sine o angle o incidence to the sine o the angle o reraction is constant or a beam o particular wavelength, where and 2 are absolute reractive indices o and 2media respectively and 2 is a reractive index o second (2) medium with respect to irst () medium. Also, the requency o light remains unchanged when passing rom one medium to the other, but velocity and wavelength changes Principle o reversibility Reraction through Compound Plate: a a b b b b c c c c a a c a 2
Real and Apparent Depth Whenever an object is placed in optically denser medium, like object O placed at the bottom o the container, the ray o light starting rom object moves rom denser to rarer medium and bends away rom normal. Thus a virtual image o the object is ormed at I. Then, distance OA is called real depth and IA is called apparent depth o object. Now, AB sin i and sin r OB Using Snell s law, AB IB I rarer medium is air, then, 2 OB IB 3
I angles are small then OB OA and IB IA OA IA Real depth Apparent depth The shit in the position which takes place ater reraction rom the surace is, x OA IA OA x OA, or h x h h here h denotes the real depth o the object Total Internal Relection: This phenomenon is observed when a ray o light moves rom denser to rarer medium. When the angle o incidence in such a case is greater than the critical angle then light would be relected back into the same medium & phenomenon is called total internal relection. As the rays move rom denser to rarer medium they bends away rom the normal. I we go on increasing the angle o incidence angle o reraction also goes on increasing (according to Snell s law). At one particular angle o incidence, angle o reraction becomes 90º. The angle o incidence or which the angle o reraction is 90º is called critical angle. 4
I angle o incidence is increased urther the ray gets totally relected back into the same medium instead o reraction. At critical angle, i c, r 90. sin sin i c 90 2 or, sin Applications o Total Internal Relection: 2. Mirage Formation: It is an optical illusion which takes place in hot countries. The layers o earth in contact with the earth are hooter and rarer whereas the upper layers are colder and denser. When the ray o light moves downwards ater relection rom object like tree it is moving rom denser to rarer medium. The agle o incidence goes on increasing with reraction are each layer o atmosphere. For one particular layer the angle o incidence is greater than critical angle and the ray o light suers total internal relection back in the upward direction. Thus a virtual and inverted image o the object is ormed on the ground. These virtual images produces the impression o relection rom water due to atmospheric disturbance. 2.Diamond: Diamonds are known or their spectacular brilliance. Their brilliance is mainly due to the total internal relection o light inside them. The critical angle or diamond-air interace (about 24.4 ) is very small, thereore once light enters a diamond, it is very likely to undergo total internal relection inside it.diamonds ound in nature rarely exhibit the brilliance or which they are known. It is the technical skill o a diamond cutter which makes diamonds to sparkle so brilliantly. By cutting the diamond suitably, multiple total internal relections can be made to occur. i c 5
3. Optical Fibres : Optical ibres consists o several thousand o very long ibres o the diameter o 0 4 cm, with reractive index.7. The ibres are located with a thin layer o material o lower reractive index. Light entering rom one side undergoes about 0 2 thousand relections per meter and comes out rom other end. Optical ibres can be put to number o application ; (i) They can be used to transmit high intensity laser light insider the body. (ii) They can be used in the ield o communication in sending video signals rom one place to another. (iii) They are used to see images o body parts not clearly visible in X- Rays. 4. Prism: Prisms designed to bend light by 90º or by 80º make use o total internal relection. Such a prism is also used to invert images without changing their size 6
Reraction ormula at a spherical surace with the object in rarer medium Let be an object O placed in a rarer medium o reractive index n, on the principal axis o a spherical surace XY, o reractive index n 2 centre o curvature C, orms the real image I, in the denser medium. Let AM be perpendicular on the principal axis and α AOM,β β AIM, γ ACM From ACO, i α + γ tan α + tan γ >.. [as α & γ are small ] From ACI, γ β + r > r tan γ + tan β..2 [as β & γ are small ] Now, by Snell s law, n sin i n 2 sin r or or small angles, n i n 2 r > Since A & P are very much close to each other >. 4 Equation (4) gives us the Reraction ormula at a spherical surace with the object in rarer medium age distance and It holds or any curved spherical surace. 7
Reraction ormula at a spherical surace with the object in denser medium Lens maker's ormula Let us consider a lens made up o a medium o reractive index 2 placed in a medium o reractive index, with R and R 2 as the radii o curvature o two spherical suraces ACB & ADB respectively,p as optical centre. Let O be a point object on the principal axis o the surace ACB, o which real image is ormed at I I by it in the denser medium. The reraction ormula or the surace ACB is.. The image at I I is behaving like a virtual object or the surace ADB, thereby orming the inal image at I. The reraction ormula or the surace ADB is 2 Adding equations (2) and () Dividing the above equation by n..3 8
I the object is at ininity, the image is ormed at the ocus o the lens.i.e. u, v. Then the eq (3) becomes..4 I the reractive index o the lens is n and it is placed in air. 2 and. So the equation (5) becomes..5 This is called the lens maker's ormula. Power o a lens The power P o a lens is deined as the tangent o the angle by which it converges or diverges a beam o light alling at unit distant rom the optical center or small value o δ. Thus, P / The SI unit or power o a lens is dioptre (D) D m The power o a lens o ocal length o metre is one dioptre. Power o a lens is positive or a converging lens and negative or a diverging lens. 9
Dispersion through prism Q.:- What is angle o dispersion? ind an expression or it Ans : - The angle by which a ray o light is deviated rom its original path while passing through a prism suering reraction at its reracting suraces is known as angle o deviation Let a ray o light be incident along PQ at angle o incidence (i) on reracting surace AB o a prism. Let it be reracted angle QR angle o reraction (r ) and again be incident is the other reracting surace AC at an angle (r 2 ), which immerges along RS at an angle o emergence (e) I we proceed the emergent Ray RS in the backward direction then it will meet the original direction o light PQK at T making an angle STK δ is known as angle o deviation. From QRT, STK TQR + TRQ > δ (i r ) + (e r 2 ) > δ (i e) (r + r 2 ) ------ (i) From the quadrilateral AQNR A+ Q + N + R 360 0. > A + 90 + N + 90 360 0 > A + N 360 80 > A + N 80 ------ (ii) 0
From QNR, r + r 2 + N 80 0 ----------- (iii) From (iii) & (ii) A + N r + r 2 + N > A r + r 2 -------- (iv) Putting in equation (i) δ (i + e) A..(v) Q. What is angle o minimum deviation. Find out an expression or reractive index in terms o minimum elevation o prism ormula. Ans:- I we draw the graph between angle o incidence and angle o deviation then it is ound that with angle o incidence, angle o deviation decreases irst, becomes minimum; then again increases with the urther increase in angle o incidence as shown in i δ graph. The minimum value o angle o deviation or a ray o high passing through a prism is known as angle o minimum elevation Condition o minimum deviation : - ) The ray through the prism should be parallel to the base o the prism. 2) i e ( o incidence o emergence) 3) r r 2 The angle o elevation, rom the expression δ i + e - A (i) Where A is angle o prism. A r + r 2 ------------------ (ii)
For minimum deviation, i.e. when δ δ m i e and r r 2. > δ m i + i A m A >2i δ m + A > i δ +.. (iii) 2 (ii) > A r + r > r A 2 ----(iv) The reractive index o the material o the prism is given as sin sin i r > δm + A sin( ) 2 sin r / 2 Q. Find the condition or no emergent o light through the prism Ans. For the ray o light not to emerge through a prism r 2 i c > A r i c >A r + i c sin i sin r From sinr sini > sin i > r sin So, A sin i sin + i c.....(ii) 2
Dispersion: The phenomenon by virtue o a ray o light while passing through a prism spilts up into its constituent wavelengths, is known as dispersion. Q: Exlain why (i) violet deviates the most and red the least in the spectrum (ii) the deviation suered by dierent clours o the spectrun is dierent or dierent colours Ans: (i) By Cauchy's relation a + b/λ 2 + c/λ 2 +.. () a,b,c are constants Deviation produced by prism o small angle, δ ( - )A...(2) A is o prism From () > α / λ 2 From (2) > δ α.(4) From (3) and (4) > δ α / λ 2, Since wavelength o red is more than that o violet, so deviation produced by violet is more than that produced by red (ii) By Cauchy's relation 3
a + b/λ 2 + c/λ 2 +.. () a,b,c are constants Deviation produced by prism o small angle, δ ( - )A.(2) A is o prism From () > α / λ...(3) From (2) > δ α.(4) From (3), it is seen that or dierent colours o white light, there will be dierent values o From (4), it is seen that or dierent values o. there will be dierent values o δ. So dierent colours deviated by dierent angles o deviations. Angular dispersion The dierence o deviations produced by the two extreme colours o the sectrum is called angular dispersion. It is denoted by δ v δ r. δ v δ r ( v )A ( r )A ( v r )A.() I deviation suered by mean light is δ, δ ( ) A (2) () and (2) > δ v δ δ r v ) ω ( ) ( r where ω is called the dispersive power o prism. Dispersive power o a prism is deined as the ratio o angular dispersion to mean deviation produced by prism. As v > r, thereore, dispersive power is always positive. 4
Scattering :- When a beam o light is incident on particles o very small size, smaller than the order o wavelength o light, light proceeds in all possible directions. The phenomenon is called scattering. According to Rayleigh's law " The intensity o scattered light, having wavelength λ, varies inversely as ourth power o its wavelength." I λ 4 As λ r 2 λ b, thereore, scattering o blue colour will be 6 times more than that o light. Blue color o Sky : Being shorter wavelength, scattered blue light dominates and hence sky appears blue. Simple Microscope: Object is placed between convex lens and principal ocus an erect, virtual and magniied image is ormed on the same side o the object. In the igure AB is the object. A convex lens is producing a virtual, erect and magniied image A' B' at least distance o distinct vision. Magniying Power : It is the ratio o angle subtended by the image at the eye to the angle subtended by the object at the eye when both are placed at least distance o distinct vision. 5
Since the virtual image is ormed at least distance o distinct vision, thereore, V D. Using Lens Formula, Multiplying both sides by D, we get, From () and (2), M + D Compound Microscope: It is used where larger magniication is required. The convex lens O o short ocal length and short aperture and eye piece o short ocal and large aperature is required. Let AB be an extended object situated on the principal axis at distance greater than ocal length o the objective. As reraction takes place through the objective O, a real inverted and magniied image A B is ormed. The position o eye piece so adjusted that A B alls within its ocal length and so the inal image A B is ormed at least distance o distinct vision. Thus, inal image A B is ormed in highly magniied but is inverted with respect to the object AB. The course o rays orming the inal image. 6
Magniying Power: The magniying power is deined as the angle subtended by the inal image at the eye to the angle subtended by object when both are placed at least distance o distinct vision rom eye. M β tan β M α tanα A'' B''' A' B' M O M C A' B' AB For objective lens, v M O u Again since the lens E, acts like simple microscope, its magniication M C is given by, M + C D e 7
Thus, magniication o compound microscope should be, v M + u D e Astronomical Telescope: Device used to see very ar o heavenly bodies. The objective lens has large ocal length and large aperture. The eye piece has small ocal length and small aperture. A parallel beam o light coming rom distance object orms a real, inverted and diminished image at a distance 0 rom O. The image then acts as an object or eye piece, and inal image is ormed ater reraction through eye piece. Normal Adjustment: I the inal image is ormed at ininity ater reraction through the eye piece. The magniying power o telescope is deined as the ratio o angle b subtended by the image to the angle subtended by the object at the eye when both are placed at ininity. 8
The distance between the two lenses is ( 0 + e ). When image is at least distance o distinct vision: The objective lens orms the real inverted and diminished image A B at n. I A B orms the real image within the ocal length e o the eye piece, a inal virtual but magniied image A B is observed. The position o eye piece is so adjusted that inal image is ormed at least distance o distinct vision D rom the eye 9
Magniying Power: It is the ratio o angle subtended at the eye by the inal image ormed at least distance o distinct vision to the angle subtended by the unaided eye by the object at ininity. M β α tanβ tanα C B' C B' 2 Using Lens ormula, u M e u 0 e v e e e + + D D e + D u A' B' CB' C B' A' B' D D 2 0 u e Relecting telescopes have several advantages over reracting telescopes () There is no chromatic aberration in a mirror. (2) I a parabolic relecting surace is chosen, spherical aberration is also removed. (3) Mechanical support is much less o a problem since a mirror weighs much less than a lens o equivalent optical quality, and can be supported over its entire back surace, not just over its rim. 20
Relecting telescopes Since in a relecting telescope,the objective mirror ocuses light inside the telescope tube, so an eyepiece is used to observe the light inside o it. A paraboloidal concave mirror o aperture, equal to 200 inches (nearly 6 6 metres) is used. It is known as objective. To ocus the incident light, another secondary convex mirror is used, which now passes the light through a hole in the objective primary mirror to the eyepiece. This is known as a Cassegrain telescope, named ater its inventor. It has the advantages o a large ocal length in a short telescope. The largest telescope in India is in Kavalur, Tamil Nadu. It is a 2.34 m diameter relecting telescope (Cassegrain). It was ground, polished, set up, and is being used by the Indian Institute o Astrophysics, Bangalore. The largest relecting telescopes in the world are the pair o Keck telescopes in Hawaii,USA, with a relector o 0 metre in diameter. xxxxxxxxxxxxxxxxxxxxxxxxxxxxx 2