NCERT Solutions for class 12th Physics Chapter 9 Ray Optics and Optical Instruments

Exercise

Question 1. A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

Question 2. A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Question 3. A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

Question 4. Figures (a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass the angle of incidence in water is 45° with the normal to a water-glass interface [Fig. (c)].

Note: Refer Chapter at a Glance (8)

Question 5. A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)

Note: When angle of incidence is equal to the critical angle the ray will pass through the inte,face.

Question 6. A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be 40°. What is the refractive index of the material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.

Question 7. Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20 cm?

Question 8. A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?

Note: Proper sign convension to be used while putting the object distance (u), the image distance (v) and the focal length (I).

Question 9. An object of size 3.0 cm is placed 14 cm in front of concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

Question 10. What is the focal length of a convex lens of focal length 30 cm in contact
with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

Question 11. A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25 cm), and (b) at infinity? What is the magnifying power of the microscope in each case?

Question 12. A person with a normal near point (25 cm) using a compound microscope with objective of focal length 8.0 mm and an eyepiece of focal length 2.5 cm can bring an object placed at 9.0 mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.

Question 13. A small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?

Question 14. (a) A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?

(b) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 x 106m, and the radius of lunar orbit is 3.8 x 108m.

Question 15. Use the mirror equation to deduce that:

(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
[This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Question 16. A small pin fixed on a table top is viewed from above from a distance of 50 cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15 cm thick glass slab held parallel to the table? Refractive index of glass= 1.5. Does the answer depend on the location of the slab?

Question 17. (a) Figure shows a cross-section of a ‘light pipe’ made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure.

(b) What is the answer if there is no outer covering of the pipe?

Note: Optic fibre principle is based on the phenomena of total internal reflection

Question 18. Answer the following questions:

  • (a) You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images some circumstances? Explain.
  • (b) A virtual image, we always say, cannot be caught on a screen. Yet when we ‘see’ a virtual image, we are obviously bringing it on to the ‘screen’ (i.e., the retina) of our eye. Is there a contradiction?
  • (c) A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
  • (d) Does the apparent depth of a tank of water change if viewed obliquely?
  • If so, does the apparent depth increase or decrease?
  • (e) The refractive index of diamond is much greater than that of ordinary glass. Is this fact of some use to a diamond cutter?

Sol.

  • (a) A plane or convex mirror can produce a real image if the object is virtual: When the rays incident on a plane or a convex mirror are con­ verging to a point behind the mirror they are reflected to a point in front of the mirror on a screen.
  • (b) There is no contradiction. The convex lens of the eye produces a real image of virtual object. The Virtual image acts as an object for the eye lens.
  • (c) The fisherman looks taller to the diver because the ray of light coming from the fisherman (in air) travels from the rarer to denser medium and hence it bends towards to come from a larger distance and hence the fisherman looks taller.
  • (d) The apparent depth decreases when tank of water is viewed obliquely compared to the apparent depth when seen normally.
  • (e) Refractive index ofa diamond (about 2.4) is much larger than that of glass (about l.5)As, sin ic =1/u,the critical angle of diamond is about 24°. A diamond cutter shapes the faces of diamond such that for the angles of incidence in the range of24° to 90°, the light entering the diamond suffers TIR from many faces before getting out and hence produces a sparkling effect.

Question 19. The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3 m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

Question 20. A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.

Question 21. (a) Determine the ‘effective focal length’ of the combination of the two
lenses in 9.10, if they are placed 8.0 cm apart with their principal axes coincident. Does the answer depend on which side of the combination a beam of parallel light is incident? Is the notion of effective focal length of this system useful at all?

(b) An object 1.5 cm in size placed on the side of the convex lens in the arrangement (a) above. The distance between the object and the convex lens is 40 cm. Determine the magnification produced by the two-lens system, and the size of the image.

Note: We can not find here a simple lens equation that is true for all u and v (in terms of definite constant of the system). So, effective focal length’ is not valid here.

Question 22. At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.

Question 23. You are given prisms made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prisms which will

(a) deviate a pencil of white light without much dispersion.,
(b) disperse (and displace) a pencil of white light without much deviation.

Sol. (a) For the condition of deviation without dispersion, the first prism should be of crown glass and the second prism of flint glass. The refracting angle of the flint glass prism should be smaller than that of crown glass prism because the flint glass prism disperses more. Due to such combination the dispersion due to the first is nullified by the second.

(b) For dispersion without deviation, the flint glass prism of greater and greater angle is taken, so that deviations due to the two prisms are equal and opposite. In the combination the angle of flint glass prism will still be smaller than of crown glass because flint glass has higher refractive index than that of crown glass.

Question 24. For a normal eye, the far points at infinity and the near point of distinct vision is about 25 cm in front of the eye. The cornea of the eye provides a converging power of about 40 dioptres, and the least converging power of the eye lens behind the cornea is about 20 dioptres. From this rough data estimate the range of accommodation (i.e., the range of converging power of the eye-lens) ofa normal eye.

Sol. Here the least converging power of eye lens is given as 20 diopters behind the cornea. If we can calculate the maximum converging power, then we can get the range of accommodation of a normal eye.

Question 25. Does short-sightedness (myopia) or long-sightedness (hypermetropia) imply necessarily that the eye has partially lost its ability of accommodation? If not, what might cause these defects of vision?

Sol. No. A person with normal ability of accommodation may be myopia or hyperopic due to deflective eye structure. When the eye ball from front to back gets too elongated the “myopic” defect occur, similarly when the eye ball from front to back gets too shortened the “hypermetropia” defect occur. When the eye ball has normal length but the eye lens loses partially its ability of accommodation, the defect is called “presbyopia” and is corrected in the same manner as myopia or hypermetropia.

Question 26. A myopic person has been using spectacles of power – 1.0 diopter for distant vision. During old age he also needs to use separate reading glass of power+ 2.0 diopters. Explain what may have happened.

Question 27. A person looking at a person wearing a shirt with a pattern comprising vertical and horizontal lines is able to see the vertical lines more distinctly than the horizontal ones. What is this defect due to? How is such a defect of vision corrected?

Sol.This defect is called astigmation. It arises due to non spherical cornea. The eye lens is ideally spherical and has same curvature in different planes, but in an astigmatic eye due to non spherical cornea the curvature may be insufficient in different planes.

In the given situation the curvature in the vertical plane is enough, so vertical lines are visible distinctly. But the curvature is insufficient in the horizontal plane, hence horizontal lines appear blurred. The defect can be corrected by using a cylindrical lens with its axis along vertical. The parallel rays in the vertical plane will suffer no extra refraction but the parallel rays in the horizontal plane will be refracted largely and converges at the retina, according to the requirements to form the clear image of horizontal lines.

Question 28. A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm.

(a) What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
(b) What is the maximum and the minimum angular magnification (magnification power) possible using the above simple microscope?

Question 29. A card sheet divided into squares each of size 1 mm2 is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 10 cm) held close to the eye.

(a) What is the magnification produced by the lens? How much is the area of each square in the virtual image?
(b) What is the angular magnification (magnifying power) of the lens?
(c) Is the magnification in (a) equal to the magnifying power in (b)? Explain.

Question 30. (a) At what distance should the lens be held from the figure in Exercise 9.29 in order to view the squares distinctly with the maximum possible magnifying power?
(b) What is the magnification in this case?
(c) Is the magnification equal to the magnifying power in this case? Explain.

Question 31. What should be the distance between the object in Exercise 9.30 and the magnifying glass if the virtual image of each square in the figure is to have an area of 6.25 mm2. Would you be able to see the squares distinctly with your eyes very close to the magnifier?

Exercises 9.29 to 9.31 will help you clearly understand the difference between magnification in absolute size and the angular magnification (or magnifying power) of an instrument.}

Question 32. Answer the following questions:

  • (a) The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?
  • (b) In viewing through a magnifying glass, one usually positions one’s eyes very close to the lens. Does angular magnification change if the eye is moved back?
  • (c) Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?
  • (d) Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
  • (e) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece?

Sol. (a) The angular size of the image is equal to the angular size of the object. By using a magnifying glass, the object can be placed much closer than 25 cm. The closer object has larger angular size than the same object at 25 cm. Thus angular magnification is achieved.
(b) The angular magnification changes, if the eye moved back.
It decreases a little because the angle subtended at the eye is then slightly less than angle subtended at the lens.
(c) First, it is difficult to grind lens of very small focal length. Secondly, if we decrease the focal length of a lens, both spherical and chromatic aberrations become more pronounced.

(e) The image of the objective in the eye-piece is known as the eye-ring. If we place our eyes too close to the eye-piece, we shall not collect much of the light and also reduce our field of view. The location of the eye-ring depends on the separation between the objective and the eyepiece.

Question 33. An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?

Question 34. A small telescope has an objective lens of focal length 140 cm and an eye piece of focal length 5.0 cm. What is the magnifying power of the telescope for viewing distant objects when

(a) the telescope is in normal adjustment (ie. when the final image is at infinity)?
(b) the final image is formed at the least distance of distinct vision (25 cm)?

Question 35. (a) For the telescope described in Exercise 9.34 (a), what is the separation between the objective lens and the eyepiece?
(b) If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?
(c) What is the height of the final image of the tower if it is formed at 25 cm?

Question 36. A Cassegrain telescope uses two mirrors as shown in figure. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?

Question 37. Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in figure. A current in the coil produces a deflection of 3.5° of the mirror. What is the displacement of the reflected spot of light on a screen placed 1.5 m away?

Question 38. Figure shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Sol. Let us first consider the situation when no liquid between lens and plane mirror and the image is formed at 30 cm position of object.
As the image is formed on the object position itself, the object must be placed at focus of biconvex lens.

Now a liquid is filled between lens and plane mirror and the image is formed at position of object at 45 cm.
The image is formed on the position of object itself, the object must be placed at focus of equivalent lens of Biconvex of glass and Plano convex lens of liquid.

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