NCERT-XII / Unit- 09 Ray Optics

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Vernon Mitchell
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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).

1 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.

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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 > A N > A + N > A + N (ii) 0

11 From QNR, r + r 2 + N (iii) From (iii) & (ii) A + N r + r 2 + N > A r + r (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 (ii)

12 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 (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

13 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 () 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

14 a + b/λ 2 + c/λ () 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

15 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

16 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

17 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

18 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

19 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

20 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.

21 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

LESSON RAY OPTICS Introduction Note Ray of light Beam of light Reflection of Light by Spherical Mirrors Law of reflection Note:

2 LESSON RAY OPTICS Introduction Electromagnetic radiation belonging to the region of the electromagnetic spectrum (wavelength of about 400 nm to 750 nm) is called light. Nature has endowed the human eye