RAY OPTICS BY UMESH TYAGI

Transcription

1 Ray Optics Ray of Light: The straight line path along which the light travels in a homogeneous medium is called a ray of light. The arrow head on the ray gives us the direction of light and number of rays combined together is called beam of light. Refraction: The phenomenon in which ray of light traveling from one medium to another medium of different optical density, deviates from its original straight line path is called refraction of light. When light moves from rarer to denser medium it bends towards the normal and when it moves from denser to rarer medium it bends away from the normal. Refraction of light occurs because the speed of light changes as one moves from one medium to another. Also, the wavelength of light changes, but frequency and phase of the wave remains constant on refraction i.e. no change in phase or frequency occurs. Laws of Refraction: First Law [Snell s Law]-The ratio of the sine of angle of incidence to the sine of angle of refraction is constant for a pair of media in contact. This constant is equal to the refractive index of second medium w.r.t. first medium. The first medium is one in which incident ray lies and the second medium is one in which the refractive ray lie. If and denotes the refractive index for the two mediums then sin i sin r Second law:the incident ray, refracted ray and normal all three lie in the same plane which is plane perpendicular to the refracting surface. Absolute Refractive Index-Absolute refractive index of the medium is the ratio of velocity of light in vacuum to the velocity of light in that medium speed of light in vacuum c Absolute refractive index am speed of light in medium v RAY OPTICS BY UMESH TYAGI

2 This implies that the velocity of light decreases if the medium changes times. Relative Refractive Index-The relative refractive index of second medium w.r.t first medium is defined as the ratio of the speed of light in first medium to second medium. speed of light in first medium v speed of light in second medium v Real and Apparent Depth - Whenever an object is placed in optically denser medium, like object O placed at the bottom of the container, the ray of light starting from object moves from denser to rarer medium and bends away from normal. Thus a virtual image of the object is formed at I. Then, distance OA is called real depth and IA is called apparent depth of object. AB Now, sin i and sin r OB AB IB Using Snell s law, sin i AB OB IB IB sin r OB OB AB IB If angles are small then OB OA and IB IA Here, t denotes the real depth of the object. Lateral Shift-It is the perpendicular distance between the incident ray and the emergent ray. In BNC, BN ( BC)cos r BC t / cos r () OA Realdepth IA Appare ntde pth OA t Normal Shif, x OA IA OA t x = t - μ In BCF, CF ( BC)sin(i r) () From equation () and (), we get- t A RAY OPTICS BY UMESH TYAGI i B N N r (i-r) C d e=i F D E

3 d t sin(i r) cos r Factors- (i) Thickness of medium, (ii) Angle of incidence and (iii) Nature of medium i.e. refractive index. Refraction through Compound Plate: Consider a compound plate made of two materials with refractive index b and c ( c > b ). A ray of light incident on ray moving from rarer to denser medium bends towards the normal. Using Snell s law, a b sini sinr Similarly, at face M M it suffers refraction and using Snell s law, sinr sinr b c Finally at surface M M it suffers refraction and comes out parallel to incident ray as all the refracting surfaces are parallel. sinr sinr c a Multiply, all three equations, a a b b b b c c c c a a c a Total Internal Reflection: This phenomenon in which a ray of light is reflected back into the same medium when enters from denser to rarer medium and the angle of incidence is greater than the critical angle is called as the total internal reflection. Consider a source of light S situated in denser medium say water. As the rays move from denser to rarer medium they bends away from the normal. If we go on increasing the angle of incidence angle of refraction also goes on increasing (according to Snell s law). At one particular angle of incidence, angle of refraction becomes 90º. The angle of incidence for which the angle of refraction is 90º is called critical angle. RAY OPTICS BY UMESH TYAGI 3

4 If angle of incidence is increased further the ray gets totally reflected back into the same medium instead of refraction. At critical angle, i c, r = 90. sinic sin90 sini Applications of Total Internal Reflection:.Mirage Formation: It is an optical illusion which takes place in hot countries. The layers of earth in contact with the earth are hooter and rarer whereas the upper layers are colder and denser. When the ray of light moves downwards after reflection from object like tree it moves from denser to rarer medium. The angle of incidence goes on increasing with refraction from each layer of atmosphere. At a particular layer, the angle of incidence becomes greater than critical angle and the ray of light suffers total internal reflection. Thus, a virtual and inverted image of the object is formed on the ground. These virtual images produces the impression of reflection from water due to atmospheric disturbance. c. Optical Fibers: Optical fibers are the very long and fine threadsmade of quartz or glass. (Diameter of 0 4 cm, with refractive index.7). These threads are coated with a thin layer of material of lower refractive index. This coating is called as cladding. Ray of light entering from one side undergoes about 0 - thousand reflections per meter and comes out from other end. Optical fibers can be put to number of application; (i) They can be used to transmit high intensity laser light insider the body. RAY OPTICS BY UMESH TYAGI 4

5 (ii) They can be used in the field of communication in sending video and audio signals from one place to another. (iii) They are used in endoscopy to see images of body s internal parts (3) Totally Reflecting Prism- An isosceles right angle prism acts as a totally reflecting prism and it works on the principle of TIR. This prism can be used to deviate the rays of light by 900 or 800. It can also be used to invert the erect image of an object. Deviation by 90 0 Deviation by 80 0 Refraction through Spherical Surfaces: A spherical surface is formed if the refracting surface forms the part of a sphere. The surface is said to be convex if it bulges towards the rarer medium side and it is concave surface if it bulges towards denser medium side. Sign Conventions:. All the distances are measured from pole of spherical surfaces.. The distances measured in the direction of incident ray are taken as positive while opposite of it are taken as negative. Assumptions:. The objects are assumed to be point objects lying on the principal axis.. The aperture of spherical surface is small. 3. Incident ray, refracted ray and normal makes very small angle with principal axis. RAY OPTICS BY UMESH TYAGI 5

6 () WhenRay of light Moving from Rarer to Denser Medium: a)with convex surface towards rarer (Real Image): Consider an object O lying on the principal axis. The ray moves from rarer to denser medium and it bends towards the normal and the bending is just sufficient to make the refracted ray meets the principal axis at I. The refracted ray makes angle β with the principal axis and r with the normal. Using Snell's law, sin i sinr If angle of incident and refraction are small, then, sin i i and sin r r i r () In OAC i = + and In IAC r = (because exterior angles are equal to interior opposite angles) Putting the values of I and r in equation () ( + ) = () = + () As angle, and are small, RAY OPTICS BY UMESH TYAGI 6

7 tan tan tan AP ' AP ' OP' OP AP ' AP ' IP ' IP AP ' AP ' CP ' CP (as apertureissmall, OP' OP, AP' AP, CP' CP ) Substituting these values in (), we obtain, MP ' CP R MP MP OP IP u v (b) With convex surface towards rarer (Virtual Image): In this case incident ray OA moving from rarer to denser bends towards the normal but the bending is not sufficient to make it move towards principal axis. Thus, a virtual image of object is formed at I. Using Snell's law, sini sinr If the angle of incidence and refraction are small then sin i ~ i and sin r ~ r, i r i r Also, i = + and r = + (because exterior angles are equal to interior opposite angles) ( + ) = ( + ) ( ) = () RAY OPTICS BY UMESH TYAGI 7

8 RAY OPTICS BY UMESH TYAGI 8 Substituting the values of,, in (), we obtain () With Concave towards Rarer Medium: The ray of light starting from point object O lying on the principal axis moves towards the normal as it moves from rarer to denser medium and virtual image of the object is formed at I. Using Snell's law If the angle of incidence and refraction are small then sin i ~ i and sin r ~ r, where i = and r = () = ( + ) ( ) = + () Substituting the values of,, in (), we obtain u v R v u R IP MP OP MP CP MP ' ) ( sin sin r i r i r i

9 Similarly, we can prove the identical results for light moving from denser to rarer medium. Lens: A portion of refracting material bound between two spherical surfaces out of which at least one surface is curved is called as lens. Types of Lenses- MP MP ' MP ( ) CP OP IP R u v R v u (i) Convex or Conversing lens- A lens is said to be converging if the width of the beam decreases after refraction through it. These lenses are thick at middle and thin at edges. Focal length of converging lens is taken as positive. (ii) Concave or Diverging Lens- A lens is said to diverging if the width of beam increases after refraction through it. These lenses are thin at middle and thick at edges. Focal length of diverging lens is negative. Regarding Lenses: Definitions Optical Centre: It is a point lying on the principal axis of lens within or outside it, such that ray of light passing through it goes un-deviated. If the two surfaces are of same radii of curvature then optical centre lies exactly in the centre of the lens. Radius of Curvature (R & R ): Radius of curvature of a surface of lens is defined as the radius of that sphere of which surface forms a part. Principal Axis: The line joining centre of curvature of two surfaces and passing through optical centre is called principal axis. RAY OPTICS BY UMESH TYAGI 9

10 Principal Focus: Principal focus of the lens is a point at which beam of light coming parallel to the principal axis actually converse (in case of convex lens) or appears to diverse (in case of concave lens) after refraction through lens. Focal Length: Focal length of a lens is defined as the distance between focus and optical centre. It is denoted by f. Focal Planes: to principal axis. It is the plane passing through the principal focus and perpendicular Rules for image formation- There are three rules (i) (ii) (iii) Ray moving parallel to principal axis passes through the focus after refraction. Ray passing through the focus becomes parallel to principal axis after refraction from lens. Ray passing through the optical centre goes undeviated (in case of thin lenses) Image Formation by Convex Lens- RAY OPTICS BY UMESH TYAGI 0

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12 Image Formation by Concave Lens- New Cartesian Sign Convention for spherical Lenses: (i) (ii) (iii) All distances are measured from optical centre. The distance measured in the direction of incident ray are taken as positive while the distance measured in the opposite direction of incident ray are taken as negative Heightsmeasured upwards to principal axis are taken as positive while downwards are taken as negative Lens Formula: Lens formula is a relation between focal length of lens with the distance of objects and images. For Convex lens: (For Real Image)- Let AB be the object placed on the principal axis and beyond focus F. The ray starting from A passing through optical centre goes undeviated and the ray moving parallel to principal axis passes through focus. The two ray meet at A, thus A B is the image of the object AB. RAY OPTICS BY UMESH TYAGI

13 As ABC and A B C are similar, AB A B BC BC...() Also, CDF and A B F are similar, CD A B CF FB Also, CD = AB => AB A B CF FB...() From () and (), BC B C CF FB u f v v f uf vf uv Dividing by uvf, v u f For Virtual Image: If the object lies between optical centre and the principal focus then a virtual image of the object is formed. Again as ABC and ABC are similar. RAY OPTICS BY UMESH TYAGI 3

14 AB A B AC BC...() Similarly, as CDF and ABF are similar CD A B CF FB...() From () and () and CD = AB, AC A' C CF FB u f v v f uf vf uv Dividing by uvf, v u f For Concave Lens- As ABO and A B O are similar, A' B ' OB ' () AB OB Similarly, as ODF and ABF are similar A' B ' B ' F OD OF A' B ' B ' F () as OD AB OF AB From equation () and (), we get- OB ' B ' F OB OF OB ' OF OB ' OB OF Using sign convention- RAY OPTICS BY UMESH TYAGI 4

15 v f ( v) u f v f v u f vf uf uv Dividing by uvf on both sides- f v u Linear Magnification: The linear magnification produced by a lens is the ratio of size of the image to the size of the object. m For virtual image, sizeof image(a' B') sizeof object (AB) m h h v u A' C ( from ()) AC ( for real image ) m h h v u Thus, for a convex lens, linear magnification is positive when image is virtual and negative if image is real. Similarly, for concave lens the linear magnification is always positive. m h h v u Lens Maker s formula:this formula is used by the manufacturers to design lenses of required focal length from a glass of given refractive index. ( ) f R R Assumptions made in the derivation of lens maker s formula- (i) (ii) (iii) (iv) Lens is very thin. The aperture of the lens is small. Object is in the form of a point situated at the principal axis. Incident and refracted rays makes small angles with principal axis New Cartesian Sign Convention RAY OPTICS BY UMESH TYAGI 5

16 (i) (ii) (iii) All distances are measured from optical centre. The distance measured in the direction of incident ray are taken as positive. The distance measured in the opposite direction of incident ray are taken as negative Consider a thin lens with optical centre C, and the point object O placed on the principal axis of this lens.if the second surface AP B were absent then first surface AP B will form the real image of object O.at I. Thus () v u R But actually the second surface is present there so I acts as an imaginary object for the surface AP Bwhich forms the final image at I. Thus we can write () v v R Adding equation () and (), we get v u v v R R v u R R v u R R If the object is placed at infinity (u= ), the image will be formed at the focus, i.e. v f. f R R f R R = μ - - f R R This is lens maker s formula and is the refractive index of lens w. r. t. its surrounding s medium. RAY OPTICS BY UMESH TYAGI 6

17 Similarly, the relation can be proved for concave lens also. Power of a Lens: Power of lens is the ability of the lens to converge or diverge a beam of light falling on it. Mathematically, it is defined as the reciprocal of focal length, i.e. P f S.I.unit of power is Dioptre (D), if focal length is measured in meters. P f ( in meters) Dioptre Or P 00 f ( in cms.) Dioptre Thus one diopter is the power of a lens of focal length meter. A number of lenses can be combined to increase the magnification (compound microscope), make the final image erect (terrestrial telescope). As each lens has its own magnifying power, the resultant magnification is the product of magnification of individual lenses i.e. m = m m..... m n Lenses in Contact: Equivalent Focal Length-Suppose two lenses L and L of focal lengths f and f are placed in contact to each other as shown in figure. L L Let O be a point object on the principal axis of the lens system. In the absence of lens L, the first lens L will form a real image of object O at I. Using lens formula C C O I I v u v () f v ' u But actually the second lens is present there so the image I acts as a virtual object for second lens L which forms its real image at I. RAY OPTICS BY UMESH TYAGI 7

18 Thus again using lens formula () f v v ' Adding the equation () and (), we get, (3) f f v u If f is the equivalent focal length of the combination, then (4) f v u From equation (3) and (4). We find that f f f Equivalent power, P P P For n thin lenses in contact, we have... f f f f3 f n Equivalent power, P P P P3... P n Note- If the lenses are separated by a distance d then their equivalent focal length is given by- d and Power, P P P d P P f f f f f Refraction through Prism: A prism is a wedge shaped body made from refracting medium bound by two plane faces inclined to each other at same angle. The two plane faces are refracting surfaces and angle between them is known as the angle of prism. RAY OPTICS BY UMESH TYAGI 8

19 Consider ABC as the prism with AB and AC as the two refracting surfaces. The incident ray PE meets the refracting face AB at E making an angle of incidence i with normal NN. As it is moving from rarer to denser medium it bends towards the normal making an angle r. Similarly, at second face itmoves from denser to rarer medium making an angle of incidence r and angle of refraction e (or angle of emergence). The angle between incident and refracted ray is called angle of deviation. FOM FMO ( i r ) ( e r ) (i e) (r r ) () Again in quadrilateral AOPM, AOP OPM PMA MAO OPM 90 A 360 OPM A 80 () Also in OPM, r r OPM 80 (3) From () and (3), we get A r r (4) Now from equation () and (4), we can find out that i e A (5) For prism having small refracting angle A the incident ray makes small angle with prism, thus angle of refraction is also small. Applying Snell s law, for refraction at face AB and AC, sin i sin r and sin e sin r RAY OPTICS BY UMESH TYAGI 9

20 If the angle of incidence and refraction are small, then i r and e r Therefore from equation (5), ( r r ) A ( ) A Factors on which angle of deviation depends: (i) The angle of incidence (ii) The refractive index of the material of prism (iii) The wavelength of the light used (iv) The angle of prism Angle of Minimum Deviation: Prism Formula- The minimum value of angle of deviation when ray of light passes through the prism is called the angle of minimum deviation. In minimum deviation position, The adjacent graph shows the variation δof with the angle of incidence I for a given prism and for a given colour of light and the angle δ depends on i only. The graph shows that as i increases, the angle δ decreases and reaches a minimum value δmand the increases. The minimum value of the angle of deviation suffered by a ray on passing through a prism is called the angle of minimum deviation and denoted byδm or D m. In the position of minimum deviation it is found that i e and r r from A r, A r we get r and from i e A we have, i i A i A m m Using Snell s law, sin i sin r A+δ sin m μ= A Sin Dispersion of Light: RAY OPTICS BY UMESH TYAGI 0

21 The phenomenon of the splitting of a ray of light into its constituent colours on passing through a prism, is called as dispersion of light. Cause of dispersion. The refractive index μ of a material for wavelength λ is given the Cauchy s relation B C A 4 Where A, B and C are the constants which depends upon the nature of material. Also, for small angled prism, the angle of deviation is given by ( )A Now and hence R R R V R V Thus the red colour is deviated the least and the violet is deviated the most. Other colours are deviated by angles between red and violet. So different colours of white light det dispersed on refraction through a prism. Angular Dispersion: This difference of deviation produced in violet and red light is called angular dispersion. Angular dispersion, Dispersive Power: V R ( ) A ( ) A V ( ) A V R R It is the ability of the prism material to cause dispersion and it is defined as the ratio of the angular dispersion to the mean deviation (i.e. deviation of yellow colour). It is denoted by ω. Angular dispersion V R V R Dispersive Power, Mean deviation RAY OPTICS BY UMESH TYAGI

22 δ V + δr Note- () δy or δ = () As v > r, therefore, dispersive power is always positive. Scattering of Light: The phenomenon of the change in direction of light due to the atmospheric particles is called as scattering of light. Intensity of scatted light depends upon the size of particles. If the size of particles is much smaller than the wavelength of light then Rayleigh law holds good and according to this law, The intensity of scattered light is inversely proportional to the fourth power of its wavelength." i.e. I 4 If the size of particles (like water droplets in clouds) is larger than the wavelength of light then Rayleigh law does not remain valid and all colours are equally scattered..applications of Scattering of light- Blue color of Sky: Blue colour of the sky. Blue colour of the sky is due to scattering of sunlight by air molecules. According to Rayleigh's law, intensity of scattered light, 4 I.So blue light ofshorter wavelength is scattered much more than red light of longer Wavelength. When we look atthe sky, the scattered light enters our eyes and this light contains blue component in a large proportion. That is why the sky appears blue. Note-() As r = b, therefore, scattering of blue colour will be 6 times more than that of red light. Thus the scattered intensity is maximum for shorter wavelengths () Moon has no atmosphere. There is no scattering of sunlight. The sky appears dark. Reddishness at Sunset and Sunrise. During sunrise or sunset, the sun is near the horizon. Sunlight has to travel a greater distance. So shorter waves of blue region are scattered away by the atmosphere. Red waves of longer wavelength are least scattered and reach the observer. So the sun appears red. Clouds appear white. Large particles like raindrops, dust and ice particles do notscatter light in accordance with Rayleigh's law, i.e., their scattering power is not selective. Theyscatter light of all colours almost equally. Hence the clouds which have droplets of water witha >>λ are generally white. RAY OPTICS BY UMESH TYAGI

23 Danger signals are red. According to Rayleigh's law, the intensity of scattered light is inversely proportional to the fourth power of Wavelength. In the visible spectrum, red colour has the largest wavelength, it is scattered the least. Even in foggy conditions, such a signal covers large distances without any appreciable loss of intensity due to scattering. Therefore, red coloured signals are preferred. Rainbows: The rainbow is nature s most spectacular display of the spectrum of light, produced by refraction, dispersion and internal reflection of sunlight by spherical rain drops. It is observed when the sun shines on rain drops, during or after a shower. An observer standing with his back towards the sun observes in the form of concentric circular arcs (bows) of different colours in the horizon. The inner brighter rainbow is called the primary rainbowand the outer fainter rainbow is called the secondary rainbow. The primary rainbow is formed by rays which undergo one internal reflection and tworefractions and finally emerge from the raindrops at minimum deviation. The red rays emergefrom the water drops at one angle of 43 and theviolet rays emerge at another angle of 4. Theparallel beam of sunlight getting dispersed atthese angles produces a cone of rays at theobserver s eye, as shown in Fig. Thus therainbow is seen as a colourful arc, with its inneredge violet and outer edge red in colour. The secondary rainbow is formed by therays which undergo two internal reflections andtwo refractions before emerging from the waterdrops at minimum deviation. Due to two internalreflections, the sequence of colour in secondaryrainbow is opposite to that in the primaryrainbow. Here the inner red rays emerge from thewater drops at angle of 5 and the outer violetrays emerge at angle of 54. RAY OPTICS BY UMESH TYAGI 3

24 Optical Instruments The instruments used to see the tiny or heavenly bodies are known as optical instruments. Simple Microscope: A convex lens of short focal length acts as a simple microscope when the object is placed between the optical centre and focus of the lens. In this position of object convex lens forms the magnified image behind the object. In the figure object AB which when viewed by an unaided eye cannot be seen distinctly. A convex lens is then interposed between the eye and the object so that the distance 'u' of the object from the lens is less than the focal length of the lens. A virtual, erect and magnified image A'B' will be produced. By adjusting the distance of object image is formed at least distance of distinct vision (D=5cm for a healthy eye). Magnifying Power: It is the ratio of 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 of distinct vision. tan Magnifying Power tan AB CB CB' D A B' CB u...() CB' Since the virtual image is formed at least distance of distinct vision (D), therefore v = - D, Using Lens Formula, RAY OPTICS BY UMESH TYAGI 4

25 v u f D u f Multiplying both sides by D, we get, D u D D u f D f...() From () and (), M D f Compound Microscope: It is used to see the tiny objects which can t be seen by naked eyes. Construction- It consists of two lenses called as objective and eyepiece. The size and focal length of objective are smaller than that of eyepiece. These lenses are fitted at one end of two hollow metallic tubes open at both ends. These tubes can be inserted into each other with the help of rack and pinion arrangement to change the distance between the two lenses. Working- Let AB be an object situated on the principal axis at distance greater than focal length of the objective. As refraction takes place through the objective O, a real inverted and magnified image A B is formed. This image acts as an object for eyepiece. The position of eye piece so adjusted that A B falls within its focal length and so the final image A B is formed at least distance of distinct vision. Thus, final image A B which is highly magnified but is inverted with respect to the object AB is formed by eyepiece. RAY OPTICS BY UMESH TYAGI 5

26 Magnifying Power: The magnifying power is defined as the angle subtended by the final image at the eye to the angle subtended by object when both are placed at least distance of distinct vision from eye. tan A ' B '/ C A ' M tan A" P / C A" AB ' ' CA" M mo me AB C A ' For objective lens, m o v u o o Again since the lens eyepiece, acts like a simple microscope, so its magnification m e is given by, m e D f e Thus, magnification of compound microscope should be, M v o uo D fe If final image is formed at infinity, then m e D f e M v o u o D f e Astronomical Refracting Telescope: Telescopes are used to see very far off heavenly bodies. Construction- It consists of two lenses called as objective lens and eyepiece. The eye piece has small focal length and small aperture than that of objective lens. These lenses are fitted at one end of two hollow metallic tubes open at both ends. These tubes can be inserted into each other with the help of rack and pinion arrangement to change the distance between the two lenses. Working- A parallel beam of light coming from distance object forms a real, inverted and diminished image at a distance f 0 from C. The image then acts as an object for eye piece, and final image is formed after refraction through eye piece. RAY OPTICS BY UMESH TYAGI 6

27 (i) Normal Adjustment: If the final image is formed at infinity after refraction through the eye piece. The magnifying power of telescope is defined as the ratio of angle β subtended by the image to the angleα subtended by the object at the eye when both are placed at infinity. tan M tan A ' B '/ C B ' CB ' M A ' B '/ C B ' C B' C B ' f focal length of objective lens C B ' f focal length of eyepiece o e M f f o e The distance between the two lenses, L fo fe. (ii) When image is at least distance of distinct vision: If A B lies within the focal length f e of the eye piece, a final virtual but magnified image A B is observed. The position of eye piece is so adjusted that final image is formed at least distance of distinct vision D from the eye. Consider a source of light S situated in denser medium say water. As the rays move from denser to rarer medium they bends away from the normal. RAY OPTICS BY UMESH TYAGI 7

28 Magnifying Power: It is the ratio of angle subtended at the eye by the final image formed at least distance of distinct vision to the angle subtended by the unaided eye by the object at infinity. M M tan A ' B '/ C B ' tan A ' B '/ C B ' CB ' fo C B' u e Using Lens formula, f v u f D u e u f D e e e Length of the tube, L fo fe Cassegrain reflecting telescope- fo fe M fo M fe D fe D It consists of a large concave paraboloidal (primary) mirror having a hole at its centre. This mirror acts as an objective and it is fitted at one end of a hollow metallic tube. There is a small convex (secondary) mirror between the focus and pole of the primary RAY OPTICS BY UMESH TYAGI 8

29 mirror. The eyepiece is placed on the axis of the telescope near the hole of the primary mirror outside the tube. Working- The parallel rays from the distant object are reflected by the large concave mirror. Before these rays come to focus at F, they are reflected by the small convex mirror and are converged to a point I just outside the hole. The final image formed at I is viewed through the eyepiece. As the first image at F is inverted with respect to the distant object and the second image I is erect with respect to the first image F, hence the final image is inverted with respect to the object. Let f 0 be the focal length of the objective and fe that of the eyepiece. For the final image formed at the least distance of distinct vision, f 0 e M f e D For the final image formed at infinity, f0 R / M f f e Advantages of reflecting type telescope over a refracting type telescope: f e (i) (ii) (iii) (iv) (v) (vi) No chromatic aberration, because mirror is used. Spherical aberration gets removed by using a paraboloidal mirror. The image is bright, because there is no loss of light due to reflection and absorption by objective. Higher resolution can be obtained by using a mirror of large aperture. A mirror provides an easier mechanical support over its entire back surface. It is difficult and expensive to make large sized lens free from chromatic aberration and distortions. Thus reflecting type telescopes are better than refracting type astronomical telescopes. * * * * * * * * * * * * * * * * * RAY OPTICS BY UMESH TYAGI 9