LJPS Gurgaon. Class XII- Physics - Assignment Topic: - Ray Optics

Transcription

1 LJPS Gurgaon 1. The refractive index of the ediu i 3. What i the angle of refraction, if the unpolaried light i incident on it at the polarizing angle of the ediu? [An : 30 degree] Cla XII- Phyic - Aignent Topic: - Ray Optic 4. A thin pri of 60 degree angle give a deviation of 30 degree. What i the refractive index of aterial pri? [An = 1.4]. In the figure given below, the path of a parallel bea of light paing through a convex len of refractive index kept in a ediu of refractive index i hown. IS (i) or( ii.) (iii) 5. The refractive index of a aterial of a concave len i n 1. It i iered in a ediu of refractive index n. A parallel bea of light in incident on the len. Trace the path of eergent ray when (i) n n1 (ii) n n1 (iii) n n1 3. In the figure given below, the path of a parallel bea of light paing through a convex len of refractive index kept in a ediu of refractive index i hown. IS (i) or( ii.) (iii) 6. The iage of an object fored by a len on the creen i not in harp focu. Sugget a ethod to get clear focuing of the iage on the creen without diturbing the poition of the object, the len or the creen. 7. Why doe the ky appear blue?

2 b. The Sun look reddih at unrie and unet a viewed fro Earth. 8. A len of focal length 30 c i cut a hown in figure. What will be the new focal length? 1. Uing the data given below, tate a to which of the given lene will you prefer to ue a (i) an eyepiece, and (ii) an objective, to contruct an atronoical telecope. Give reaon for your anwer. 9. The iage of a all electric bulb fixed at the wall of a roo i to be obtained on the oppoite wall 3 away by the ean of large convex len. What i the axiu poible focal length of the len required for the purpoe? An.0.75 Len Power Aperture L 1D L 10 D D 0.0 L 3 0 D 0.0 L A concave len ha the ae radii of curvature for both ide and ha refractive index 1.6 in air. In the econd cae, it i iered in a liquid of refractive index 1.4. Calculate the ratio of the focal length of the len in the two cae/ 13. A right angled crown gla pri with critical angle 41 degree before an object, PQ, in two poition a hown in the figure (i)and (ii) Trace the path of the ray fro P and Q paing through the pri in the two cae 11. Give reaon for the following: a. Rainbow i never oberved on the urface of the Moon. 14. A copound icrocope with an objective of 1.0 c focal length and an eye piece of.0 c focal length ha a tube length of 0 c.calculate

3 the agnifying power of the icrocope If the final iage i fored at the near point of the eye 17. A ray of light pae through an equilateral pri (refractive index 1.5) uch that angle of incidence i equal to angle of eergence and the latter i equal to 3/4 th of angle of pri. Calculate the angle of deviation. An Plot a graph to how the variation of the angle of deviation a a function of angle of incidence for the light ray paing through a pri. Write the relation for the refractive index of the pri in ter of the angle of iniu deviation and the angle of the pri. 18. Explain why doe a convex len behave a a converging len when iered in water ( 1. 33) and a a diverging len, when iered in carbon diulphide ( 1.6) 16. An object i placed in front of a right angled pri ABC in two poition (a) and (b) a hown. The pri i ade of crown gla with critical angle of 41 degree. Trace the path of two ray fro P and Q, (i) in (a) noral to the hypotenue and (ii) in (b) parallel to the hypotenue. C B P P 19. Give reaon for the following obervation ade fro earth 1. Sun i viible before the actual unrie.. Sun look reddih at unet Q Q A C B A 0. A gla pri ha a iniu angle of deviation D in air. State with reaon how the angle of iniu deviation will change, if the pri i iered in a liquid of refrective index > 1

4 1. State the condition for total internal reflection of light to take place. Calculate the peed of light in a ediu whoe critical angle i 45 degree. 8 [An: v.1 10 / ] 5. Two convex lene of ae focal length but aperture 5 c and 10 c are ued a objective lene in two atronoical telecope. 1. What will be the ratio of their reolving power?. Copare the intenity of iage fored in two cae. Violet light i incident on a converging len of focal length fstate with reaon how focal length of the len will change, if the violet light i replaced by red light. 6. A all bulb i placed at the botto of the tank containing water to a depth of 80 c. what i the area of the urface of water through which light fro the bulb can eerge out? Refractive index of water i (Conider the bulb to be a point ource). An Draw a labeled ray diagra howing the foration of iage uing a Newtonian type reflecting telecope. 7. A bea of light converge to a point P.Now a len i placed in the path of the convergent bea 1 c fro P. At what point doe the bea converge if the len i (a) a convex len of focal length 0 c. (b) a concave len of focal length 16 c? An. 48c (real iage) 4. An atronoical telecope conit of two thin lene et 36 c apart and ha agnifying power 8. Calculate the focal length of the lene. [ An: f e 4c, f 0 3c ] 8. At what angle hould a ray of light be incident on the face of a pri of refracting angle 60 degree, o that it jut uffer total internal reflection at the other face? The refractive index of the aterial of the pri i 1.54 An Ue the irror equation to deduce that: a. An object placed between f and f of a of a concave irror produce a real iage beyond f.

5 b. A convex irror alway produce a virtual iage independent of the location of the object c. The virtual iage produced by a convex irror i alway diinihed in ize and i located between the focu and the pole. d. An object placed between the pole and focu of a concave irror produce a virtual and enlarged iage. Explain, giving reaon, whether it will be have a a converging len or a diverging len in each of thee two edia. 9. A convex len ade up of gla of refractive index 1.5 i dipped, in turn in: a. ediu A of refractive index 1.65 b. ediu B of refractive index Three light ray red (R), green G, and blue B are incident on a right angled pri abc at face ab. The refractive indice of the aterial of the pri for red, green and blue wavelength are 1.39, 1.44, 1.47 repectively. Out of the three which colour ray will eerge out of face ac? Jutify your anwer. Trace the path of green G ray after paing through face ab a B G 45 R b c 30. A Ca grain telecope ue two irror a hown in figure, Such a telecope i built with the irror 0 apart. If the radiu of curvature of the large irror i 0 and all irror i 140, where will the final iage of an object at infinity be? An Two concave lene P and Q of an atronoical telecope having focal length 4c and 16 c repectively are arranged a hown in figure 1. Which of the two lene will you elect to ue a the objective len and why?. What hould be the change in the ditance between the lene to have the telecope in it noral poition. 3. Calculate the agnifying power of the telecope in the noral adjutent poition. 31. A convex len ade up of gla of refractive index 1.5 i dipped, in turn, in a. ediu A of refractive index 1.65 b. ediu B of refractive index 1.33

6 b. If thi telecope i ued to view the oon, what i the diaeter of the iage of the oon fored by the objective len? The diaeter of the oon i , and the radiu of lunar orbit i [An: c] 34. You are given three lene having power P and aperture A a follow: P 1= 6D A 1 = 3 c P = 3D A = 15 c P 3 1D A 1. 5c 3 Which two of thee will you elect to contruct (i) a telecope and (ii) a icrocope? State the bai for your anwer in each cae. 37. Find the poition of the iage by the len cobination given in the figure. 35. Figure how an equiconvex len (of refractive index 1.50) in contact with a liquid layer on top of a plane irror. A all needle with it tip on the principal axi i oved along the axi until it inverted iage i found at the poition of the needle. The ditance of the needle fro the len i eaured to be 45.0 c. The liquid i reoved and the experient i repeated. The new ditance i eaured to be 30 c. What i the refractive index of the liquid? [An: 1.33] 38. A all telecope ha an objective len of focal length 140 c and eye piece of focal length 5.0 c. a. For the telecope what i the eparation between the objective len and the eye piece? An. 145c b. If thi telecope i ued to view a 100 tall tower 3 k away what i the height of the iage fored by the objective len? An. 4.7c c. What i the height of the final iage of the tower if it i fored at 5 c?an. 8.c 36. a. A giant refracting telecope at an obervatory ha an objective len of focal length 15 If an eye piece of focal length 1.0 c i ued, what i the angular agnification of the telecope? [An: 1500] 39. Draw a labeled ray diagra of an atronoical telecope ued in the noral

7 adjutent poition. Write the expreion for it agnifying power. Two atronoical telecope T andt 1 have the ae agnifying power. The ratio of aperture of their objective i 3 : 1. Which one of the two produce iage of greater intenity?. Which one of the two ha larger reolving power? Explain your anwer in each cae. 40. Draw a ray diagra to how the foration of the iage of a point object placed in a ediu of refractive index n1 on the principal axi of a convex pherical urface of radiu of curvature R ad refractive index n.uing the diagra n n1 n n1 derive the relation where u v u R and v have their uual eaning. A converging len of focal length 50 c i placed co axially in contact with another len of unknown focal length. If the cobination of behave like a diverging len of focal length 50 c, find the power and nature of the econd len. 4. Two lene of power +15 D and -5D are in contact with each other foring a cobination len. a. What i the focal length of thi cobination? b. An object of ize 3 c i placed at 30 c fro thi cobination of lene Calculate the poition and ize of the iage fored. [An: f = 10 c, v = 15 c, I = -1.5 c] 43. With the help of a ray diagra explain the phenoenon of total internal reflection. Obtain the relation between critical angle and the refractive index of the ediu. Draw ray diagra to how how a right angled iocele pri can be ued to (i) deviate the ray through 180 degree. (ii) deviate the ray through 90 degree and (iii) invert the ray 41. A len for a real iage of an object. The ditance fro the object to the len i u c. The given graph how variation of v with u 1. What i the nature of len?. Uing, the graph, find the focal length of thi len. Draw a ray diagra to how the foration of real iage of the ae ize a that of the object placed in front of a converging len. Uing thi ray diagra etablih the relation between u, v and f for thi len.

8 44. A 4.5c needle i placed 1c away fro a convex irror of focal length 15c. Give the location of the iage and the agnification. Decribe what happen a the needle i oved farther fro the irror. An The iage i erect and virtual. A the needle i oved away fro the irror, the iage alo ove away fro the irror upto and the iage decreae in ize. eyepiece of focal length 6.5c eparated by a ditance of 15c. How far fro the objective hould an object be placed in order to obtain the final iage at (a) the leat ditance of ditinct viion (5c), and (b) at infinity? What i the agnifying power of the icrocope in each cae? An. a. 0 b A tank i filled with water to a height of 1.5c. The apparent depth of a needle lying at the botto of the tank i eaured by a icrocope to be 9.4c. What i the refractive index of water? If water i replaced by a liquid of refractive index 1.63 upto the ae height, by what ditance would the icrocope have to be oved to focu on the needle again? An. 1.7 c. 48. A all pin fixed on a table top i viewed fro above fro a ditance of 50c. by what ditance would the pin appear to be raied if it i viewed fro the ae point through a 15 c thick gla lab held parallel to the table? Refractive index of gla =1.5. Doe the anwer depend on the location of the lab? An. 5c the location of the lab will not affect the anwer. 46. An object of ize 3.0 c i placed 14c in front of a concave len of focal length 1c. Decribe the iage produced by the len. What happen if the object i oved further away fro the len? An. 1.8c 49.a.Figure how a cro-ection of a light pipe ade of a gla fibre of refractive index The outer covering of the pipe i ade of a aterial of refractive index What i the range of the angle of the incident ray with the axi of the pipe for which total reflection inide the pipe take place a hown in the figure.? b. What i the anwer if there i no outer 47. A copound icrocope conit of an objective len of focal length.0c and an converting of the pipe?

9 An.a. i ii b A convex len of focal length 1 i kept in contact with a concave len of focal length. Find the focal length of the cobination. An. F = 1 1 / An angular agnification (agnifying power) of 30X i deired uing an objective of focal length 1.5 c and an eyepiece of focal length 5 c. How will you etup the copound icrocope? An c 54. Uing the len forula, how that an object placed between the optical centre and the focu of a convex len produce a virtual and enlarged iage. An. We get v > u [Thi how that iage i enlarged. 51. How doe the angle of iniu deviation of a gla pri of refractive index 1.5change, if it i iered in a liquid of refractive index 1.3? An. It will decreae. 55.Figure how a ray of light paing through a pri. If the refracted ray QR i parallel to the bae BC, how that (i) r 1 = r = A/, (ii) angle of iniu deviation, D = i - A 5. A ray of light incident on one of the face of a gla pri of angle A ha angle of incidence A. The refracted ray in the pri trike the oppoite face which i ilvered, the reflected ray fro it retracing it path. Trace the ray diagra and find the relation between the refractive index of the aterial of the pri and the angle of the pri. An. co A 56. Two convex lene of ae focal length but of aperture A 1 and A (A < A 1 ), are ued a the objective lene in two atronoical telecope having identical eyepiece. What i the ratio of their reolving power? Which

10 telecope will you prefer and why? Give reaon. An. Telecope with aperture A1 i preferred, becaue (i) It light gathering power i ore. (ii) It reolving power i ore. 59.A ray PQ incident norally on the refracting face BA i refracted in the pri BAC ade of aterial of refractive index Coplete the path of ray through the pri. Fro which face will the ray eerge? Jutify your anwer. 57. A right angled pri ade fro a aterial of refractive index i kept in air. A ray PQ i incident norally on the ide AB of the pri a hown. Find (in ter of ) the axiu value of up to which thi incident ray necearily undergoe total internal reflection at the face AC of the pri. An. π/ in -1 (1/ ) 60. Show that a convex len produce an N tie agnified iage when the object ditance, fro the len, have agnitude ( /N). Here i the agnitude of the focal length of the len. Hence find the two value of object ditance, for which a convex len, of power.5d, will produce an iage that i four tie a large a the object? An. 30c. 58. The following data wa recorded for value of object ditance and the correponding value of iage ditance in the experient on tudy of real iage foration by a convex len of power + 5D. One of thee obervation i incorrect. Identify thi obervation and give reaon for your choice. S.No. Object ditance (c) An. F=0c iage ditance (c) 61. a. Draw a labeled ray diagra ray diagra of a copound icrocope. b. Derive an expreion for it agnifying power. c. Why i objective of a icrocope of hort aperture and hort focal length? Give reaon. 6. A thin convex len having two urface of radii of curvature R 1 and R i ade of a aterial of refractive index. It i kept in a ediu of refractive index 1. Derive, with the help of a ray diagra, the len aker

11 forula when a point object placed on the principal axi in front of the radiu of curvature R 1 produce an iage I on the other ide of the len. An. 1 f 1 ( -I) R1 1 R 66. How uch water hould be filled in a container 1c in height, o that it appear half-filled when viewed fro the top of the container. ( a w =4/3)? An. 1 c 63. How would you etiate rough focal length of a converging len? Draw a ray diagra to how iage foration by a diverging len. Uing thi diagra, derive the relation between object ditance, iage ditance v and focal length f of the len. Sketch the graph between 1/ and 1/v for thi len. An. 1/f= 1/v 1/u. 67. How doe the refractive index of a tranparent ediu depend on the wavelength of incident light ued? Velocity of light in gla i x 10 8 / and in air i 3 x 10 8 /. If the ray of light pae fro gla to air, calculate the value of critical angle. An A ray of light pae through an equilateral pri (refractive index 1.5) uch that angle of incidence i equal to angle of eergence and the latter i equal to 3/4 th of angle of pri. Calculate the angle of deviation. An Velocity of light in a liquid i 1.8 x Find by how uch the botto of veel containing thi liquid appear to be raied if the depth of the liquid i 5c. An. 10.0c 65. A light ray pae fro air into a liquid a hown in figure. Find refractive index of liquid. An An object i placed 15c in front of a convex len of focal 10c. Find the nature and poition of the iage fored. Where hould

12 a concave irror of radiu of curvature 0c be placed o that the final iage i fored at the poition of the object itelf? An. v = +30c 74. A ray of light pae through an equilateral gla pri, uch that that the angle of incidence i equal to the angle of eergence. If the angle of eergence i ¾ tie the angle of pri, calculate the refractive index of the gla pri. An A creen i placed 80c fro an object. The iage of the object on the creen i fored by a convex len at two different location, eparated by 10c. Calculate the focal length of the len ued. An. 19.7c. 75. A convex len, of focal length 0c, ha a point object placed on it principle axi at ditance of 40c fro it. A plane irror i placed 30c behind the convex len. Locate the poition of iage fored by thi cobination. an. v = +40c 71. Trace the path of a ray of light paing through a gla pri (ABC) a hown in the figure. If the refractive index of gla i 3, find out the value of the angle of eergence fro the pri. An A convex len i placed in contact with a plane irror. An axial point object, at a ditance of 0 c fro thi cobination, ha it iage coinciding with itelf. What i the focal length of the convex len? An. 0c 7. You are given three lene L 1, L and L 3 each of focal length 10c. An object i kept at 15c in front of L 1, a hown. The final real iage i fored at the focu I of L 3. Find the eparation between L 1, L and L A convex len, and a convex irror, (of radiu of curvature 0c) are placed co-axially with the convex irror placed at a ditance of 30c fro the len. For a point object at a ditance of 0c fro the len, the final iage, due to thi cobination, coincide with the object itelf. What i the focal length of the convex len?

13 An c. 78. One face of a pri with a refracting angle of 30 0 i coated with ilver. A ray incident on another face at an angle of 45 0 i refracted and reflected fro the ilver coated face and retrace it path. Find the refractive index of the aterial of the pri. An. 8. Draw a cheatic ray diagra of reflecting telecope howing how ray coing fro a ditant object are received at the eyepiece. Write it two iportant advantage over a refracting telecope. 79. A hort object of length L i placed along the principal axi of a concave irror away fro focu. The object ditance i. If the irror ha a focal length f. What will be the length of the iage? you ay take L <<Iv f I. f An. L = L ( u f ) 83. Draw a ray diagra for the foration of iage by a copound icrocope. Define it agnifying power. Deduce the expreion for the agnifying power of the icrocope. 84. Draw a ray diagra howing the iage foration of a ditant object by a refracting telecope. Define it agnifying power and write the two iportant factor conidered to increae the agnifying power. Decribe briefly the two ain liitation and explain how far thee can be iniized in a reflecting telecope. 80. A obile phone lie along the principal axi of a concave irror. Show, with the help of a uitable diagra, the foration of it iage. Explain why agnification i not unifor. 81. Draw a labeled ray diagra of a refraction type telecope in noral adjutent. 85. Draw an atronoical telecope, when the final iage i fored at the leat ditance of ditinct viion (D) fro the eye. Define the agnifying power of the atronoical telecope and derive it forula.. Draw a labeled ray diagra of an atronoical telecope for the near point adjutent. You are given three lene of power 0.5D, 4D, 10D.

14 State, with reaon, which two lene will you elect for contructing a good atronoical telecope. Calculate the reolving power of thi telecope, auing the diaeter of the objective len to be 6c and the wavelength of light ued to be 540n.