CHAPTER -9 RAY OPTICS AND OPTICAL INSTRUMENTS

If light passes near a massive object, the gravitational interaction
causes a bending of the ray. This can be thought of as happening
due to a change in the effective refrative index of the medium
given by
n(r) = 1 + 2 GM/rc2
where r is the distance of the point of consideration from the centre
of the mass of the massive body, G is the universal gravitational
constant, M the mass of the body and c the speed of light in
vacuum. Considering a spherical object find the deviation of the
ray from the original path as it grazes the object.

If light passes near a massive object, the gravitational interaction
causes a bending of the ray. This can be thought of as happening
due to a change in the effective refrative index of the medium
given by
n(r) = 1 + 2 GM/rc2

The mixture a pure liquid and a solution in a long vertical column
(i.e, horizontal dimensions << vertical dimensions) produces
diffusion of solute particles and hence a refractive index gradient
along the vertical dimension. A ray of light entering the column at
right angles to the vertical is deviated from its original path. Find
the deviation in travelling a horizontal distance d << h, the height
of the column.

A myopic adult has a far point at 0.1 m. His power of accomodation
is 4 diopters. (i) What power lenses are required to see distant 

objects? (ii) What is his near point without glasses? (iii) What is
his near point with glasses? (Take the image distance from the
lens of the eye to the retina to be 2 cm.)

In many experimental set-ups the source and screen are fixed at
a distance say D and the lens is movable. Show that there are two
positions for the lens for which an image is formed on the screen.
Find the distance between these points and the ratio of the image
sizes for these two points.

A thin convex lens of focal length 25 cm is cut into two pieces
0.5 cm above the principal axis. The top part is placed at (0,0) and
an object placed at (–50 cm, 0). Find the coordinates of the image.

A short object of length L is placed along the principal axis of a
concave mirror away from focus. The object distance is u. If the
mirror has a focal length f, what will be the length of the image?
You may take L <<|v - f|.

An unsymmetrical double convex thin lens forms the image of a
point object on its axis. Will the position of the image change if
the lens is reversed?

The near vision of an average person is 25cm. To view an object
with an angular magnification of 10, what should be the power of
the microscope?

Will the focal length of a lens for red light be more, same or less
than that for blue light?

1. The rays of light falling on a convex lens in a direction parallel to principal axis of the lens, get refracted through the lens and meet actually at a single point F on the principal axis of the lens. This point is called principal focus of the lens.

Read the above passage and answer the following questions:

a)      Is principal focus of a convex lens, a real point?  Is the same true for a concave lens?

b)      A distinct image of a distant tree is obtained on a screen held at 40cm from a convex lens. What is its focal length?

c)      Our teachers and parents advise us to stay focused.  What does it imply? 

1. Mona and Anushka are friends, both studying in class 12. Mona is in Science stream and Anushka is in Arts stream. Both of them go to market to purchase sunglasses. Anushka feels that any coloured glasses with fancy look are good enough. Mona tells her to look for UV protection glasses, Polaroid glasses and photo sensitive glasses.

Read the above passage and answer the following questions:

a)      What are UV protection glasses, Polaroid glasses and photo sensitive glasses?

b)      What values are displayed by Mona? 

1. Shweta’s grandmother often complains of headache. Shweta asked her to visit an eye specialist for a check up, but she refused saying that her eye sight is O.K. Some other day, her grandmother asked Shweta to thread a needle. Shweta understood her problem and took her to the eye specialist who prescribed her spectacles of suitable power.

Read the above passage and answer the following questions:

            What could Shweta make out?

            Can you guess the nature of lens prescribed?

            What values are displayed by Shweta? 

1. 1.       Draw a ray diagram of compound microscope. Write the expression for its magnifying power.

1. 1.       State briefly two features which can distinguish the characteristic features of an interference pattern from those observed in diffraction pattern. 

1. 1.       Write down the conditions to obtain the sustained interference fringe pattern of light. What is the effect on the interference fringes in Young’s double slit experiment, when monochromatic source is replaced by a source of white light?

1. 1.       Write the condition necessary for diffraction to occur. Draw the intensity distribution curve in single slit diffraction pattern.

1. 1.       i) State the principle on which the working of an optical fiber is based.

(ii) What are the necessary conditions for this phenomenon to occur?

1. 1.       Two convex lens of same focal length but of aperture A1 and A2 (A2<A1), are used as objective lenses in two astronomical telescopes having identical lenses. What is the ratio of their resolving power? Which telescope will you prefer and why?

1. 1.       In single slit diffraction pattern a slit of width‘d’ is illuminated with red light of wavelength 650nm. For what value of‘d’ will

(i)                 The first minima fall at an angle of diffraction of 30⁰.

(ii)               The first maxima fall at an angle of diffraction of 30⁰.

1. 1.       How will the angular separation and visibility of fringes in Young’s double slit experiment change when (i) screen is moved away from the plane of the slits, and

(ii) width of the source slit is increased? 

1. 1.       Define resolving power of a telescope. How does it get affected on

(i) Increasing the aperture of the objective lens?

(ii) Increasing the focal length of the objective lens? 

1. 1.       Define resolving power of a compound microscope. How does the resolving power of a compound microscope change when

(i) Refractive index of the medium between the object and objective lens increases?

(ii) Wavelength of the radiation used is increased? 

Draw a labeled ray diagram to show the image formation in a refracting type astronomical telescope. Why should the diameter of the objective of a telescope be large?

A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens?

Two independent monochromatic sources of light cannot produce a sustained interference pattern’. Give reason.

A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of thiscombination has its image coinciding with itself. What is the focal length of the lens?

You are given following three lenses. Which two lens you will use to make objective and eyepiece of an astronomical telescope?

Under what condition does a convex lens of glass having certain refractive index, acts as a plane glass sheet?

In a single-slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? 

Unpolarised light is on a plane incident glass surface. What should be the angle of incidence so that the reflected and refracted rays are perpendicular to each other?

When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the samefrequency as the incident frequency. Explain why?

How does resolving power of telescope change if the incident yellow light is replaced by blue light?

For the same value of angle incidence, the angles of refraction in three media A, B and C are 15°, 25° and 35° respectively. In which medium would the velocity of light be minimum? 

When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed   imply a decrease in the energy carried by the light wave? Justify your answer. 

How does the fringe width, in Young’s double-slit experiment, change when the distance of separation between the slits and screen is doubled? 

1. How does the angular separation between fringes in single-slit diffraction experiment change when the distance of separation between the slit and screen is doubled? 

1. Two thin lenses of power +6 D and – 2 D are in contact. What is the focal length of the combination? 

1. How the angular separation of interference fringes in Young’s double slit experiment change when the distance between the slits and screen is doubled? 

1. A diverging lens of focal length ‘F’ is cut into two identical parts each forming a plano-concave lens. What is the focal length of each part? 

1. What is the angle between the plane of polariser and analyser, in order that the intensity of transmitted through analyser reduces to half?

1. What is the geometrical shape of the wavefront when a plane wave passes through a convex lens? 

1. An object is held at the principal focus of a concave lens of focal length f. Where is the image formed? 

1. How does power of lens vary when incident red light is replaced by blue light?

1. A concave mirror, of aperture 4cm, has a point object placed on its principal axis at a distance of 10cm from the mirror. The image, formed by the mirror, is not likely to be a sharp image. State the likely reason for the same.

1. Write the relation between angle of incidence I, angle of prism A and angle of minimum deviation  for a glass prism.

Figure 9.37 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?

Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in Fig. 9.36. 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?

A Cassegrain telescope uses two mirrors as shown in Fig. 9.33. 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?

(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?

A small telescope has an objective lens of focal length 140 cm and an eyepiece 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 (i.e., when the final image

is at infinity)?

(b) the final image is formed at the least distance of distinct vision

(25 cm)?

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?

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?

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?

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?

[Note: 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.]

(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.

A card sheet divided into squares each of size 1 mm2is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 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.

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 (magnifying power) possible using the above simple microscope?

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?

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

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?

For a normal eye, the far point is at infinity and the near point of distinct vision is about 25cm 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) of a normal eye.

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

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.

(a) Determine the 'effective focal length' of the combination of the two lenses in Exercise 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 is 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

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.

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?

Answer the following questions:

(a) You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under 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?

(a) Figure 9.35 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?

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?

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.

[Note: This exercise helps you deduce algebraically properties of

images that one obtains from explicit ray diagrams.]

(a) A giant refracting telescope at an observatory has an objective lens of focal length 15 m. 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.

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?

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,

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?

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.

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

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

 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 20cm?

 A prism is made of glass of unknown refractive index. A parallel 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.

 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.)

Figures 9.34(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 when the angle of incidence in water is 45º with the normal to a water-glass interface [Fig. 9.34(c)].

A tank is filled with water to a height of 12.5 cm. The apparentdepth 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?

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

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?