Name: Physics Grade-12

Buds Public School, Dubai

NAME: PHYSICS GRADE-12

Topic- Ray Optics

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1. The image of a candle is formed by a convex lens on a screen. The lower half of the lensis painted black to make it completely opaque. Draw the ray diagram to show the image formation. How will this image be different from the one obtained when the lens is not painted black?

2. A figure divided into squares, each of size 1 mm2 is being viewed at a distance of 9cmthrough a magnifying lens of local length 10cm, held close to the eye.

(i) Draw a ray diagram showing the formation of the image.

(ii) What is the magnification produced by the lens? How much is the area of each square in the virtual image?

(iii) What is the angular magnification of the lens?

3. Draw a schematic diagram of a single optical fiber structure. Explain briefly how anoptical fiber is fabricated. Describe in brief, the mechanism of propagation of light signal

through an optical fiber.

4. A right-angled crown glass prism with critical angle 41 0 is placed before an object PQ, intwo positions as shown in the figures (i) and (ii). Trace the paths of the rays from P and Q the prisms in the two cases.

5. (a) Draw a labelled ray diagram to show the formation of an image by a compound

microscope. Write the expression for its magnifying power.

(b) How can the magnifying power be increased?

6. Draw a labelled diagram to show the image formation in an astronomical telescope. Write an expression for its magnifying power. Why should the objective lens of such a telescope have large diameter?

7. (i) Draw a labelled ray diagram of a compound microscope, showing the formation of image atthe near point of the eye.

(ii) A compound microscope uses an objective lens of focal length 4 cm and eye lens of focal length10cm. An object is placed at 6 cm from the objective lens.

(a) Calculate magnifying power of the compound microscope, if the final image is formed at the nearpoint.

(b) Calculate the length of the compound microscope also.

8. Draw a labelled ray diagram of an astronomical telescope, forming the image at infinity.

As astronomical telescope uses two lenses of powers 10 diopter, 1 diopter.

(i) State with reason, which lens is preferred as objective and eye-piece.

(ii) Calculate the magnifying power of the telescope, if the final image is formed at the near point.

(iii) How do the light gathering power and resolving power of a telescope change, if the aperture of the objective lens is doubled ?

9 a) For the same angle of incidence, the angle of refraction in two media A and B are 25̊ and 35̊ respectively. In which medium is the speed of light less?

b) A double convex lens of glass of refractive index 1.6 has its both surfaces of equal radii of curvature of 30 cm each. An object of height 5 cm is placed at a distance of 12.5 cm from the lens. Calculate the size of the image formed.

10. How does the frequency of a beam of ultraviolet light get affected when it goes from air into glass ?

A ray of light incident on an equilateral glass prism shows minimum deviation of 30°. Calculate the speed of light through the glass prism.

11. Draw a schematic diagram of a single optical fibre structure. On what principle does such a device work ? Explain the mechanism of propagation of light signal through an optical fibre.

12. Derive the relation between the focal length of a convex lens in terms of the radii of curvature of the two surfaces and refractive index of its material. Write the sign conventions and two assumptions used in the derivation of this relation

A convex lens of focal length 40 cm and a concave lens of focal length — 25 cm are kept in contact with each other. What is the value of power of this combination?

13a) Draw a ray diagram to show the working of a compound microscope. Deduce an

expression for the total magnification when the final image is formed at the near

point.

b)In a compound microscope, an object is placed at a distance of 1.5 cm from the

objective of focal length 1.25 cm. If the eye piece has a focal length of 5 cm and the

final image is formed at the near point, estimate the magnifying power of the

microscope.

14) A converging lens is kept coaxially in contact with a diverging lens – both the lenses

being of equal focal lengths. What is the focal length of the combination?

15) 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.

16) (i) Draw a neat labelled ray diagram of an astronomical telescope in normal

adjustment. Explain briefly its working.

(ii) An astronomical telescope uses two lenses of powers 10 D and 1 D. What

is its magnifying power in normal adjustment ?

17)(i) Draw a neat labelled ray diagram of a compound microscope. Explain brieflyits working.

(ii) Why must both the objective and the eye-piece of a compound microscopehave short focal lengths ?

18) An illuminated object and a screen are placed 90 cm apart. Determine the focallength and nature of the lens required to produce a clear image on the screen, twicethe size of the object.

19) Two convex lenses of same focal length but of aperture A1 and A2 (A2 < A1), areused as the objective lenses in two astronomical telescopes having identical eyepieces.What is the ratio of their resolving power? Which telescope will you prefer andwhy? Give reason.

20(a) Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.

Deduce the expression for the refractive index of glass in terms of angle of Prism and angle of minimum deviation.

21a) Obtain lens makers formula using the expression

Here the ray of light propagating from a rarer medium of refractive index (n1) to a denser medium of refractive index (n2) is incident on the convex side of spherical refracting surface of radius of curvature R.

(b) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the pole. Using this diagram, derive the magnification formula for the image formed.

22) A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in (i) a

medium of refractive index 1.65, (ii) a medium of refractive index 1.33.

(a) Will it behave as a converging or a diverging lens in the two cases ?

(b) How will its focal length change in the two media ?

23) Use the mirror equation to show that

(a) an object placed between f and 2f of a concave mirror produces a real imagebeyond 2f.

(b) a convex mirror always produces a virtual image independent of the locationof the object.

24) A compound microscope uses an objective lens of focal length 4 cm and eyepiece lens of focal length 10 cm. An object is placed at 6 cm from the objective lens. Calculate the magnifying power of the compound microscope. Also calculate the

length of the microscope.

25) A giant refracting telescope at an observatory has an objective lens of focal length

15 m. If an eyepiece lens of focal length 1.0 cm is used, find the angular magnification

of the telescope.

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 3.42 x 106 m and

the radius of the lunar orbit is 3.8 x 106 m.

26)A ray PQ is incident normally on the face AB of a triangular prism of refracting angle of 60, made of a transparent material of refractive index 2 /√3 , as shown in the figure. Trace the path of the ray as it passes through the prism. Also calculate the angle of emergence and angle of deviation.

27) Draw a ray diagram showing the formation of the image by a point object on the principal axis of a spherical convex surface separating two media of refractive indices n1 and n2, when a point source is kept in rarer medium of refractive index n1. Derive the relation between object and image distance in terms of refractive index of the medium and radius of curvature of the surface.

Hence obtain the expression for lens-maker’s formula in the case of thin convex lens.

28)A ray of light falls on a transparent sphere with centre C as shown in thefigure. The ray emerges from the sphere parallel to the line AB. Find theangle of refraction at A if refractive index of the material of the sphere is √3 .

29) Figure shows a ray of light passing through a prism. If the refracted rayQR is parallel to the base BC, show that (i) r1 = r2 = A/2, (ii) angle ofminimum deviation, Dm = 2i – A.

30) Show that the current leads the voltage in phase by П/2 in an ac circuitcontaining an ideal capacitor

31) Draw a labelled ray diagram of an astronomical telescope to showthe image formation of a distant object. Write the mainconsiderations required in selecting the objective and eyepiecelenses in order to have large magnifying power and high resolution

of the telescope.

32) A compound microscope has an objective of focal length 1.25 cmand eyepiece of focal length 5 cm. A small object is kept at 2.5 cmfrom the objective. If the final image formed is at infinity, find thedistance between the objective and the eyepiece.

When light travels from an optically denser medium to a rarer medium,why does the critical angle of incidence depend on the colour of light ?

33(a) A ray of light is incident normally on the face AB of a right-angledglass prism of refractive index aμg = 1·5. The prism is partlyimmersed in a liquid of unknown refractive index. Find the valueof refractive index of the liquid so that the ray grazes along theface BC after refraction through the prism.

(b) Trace the path of the rays if it were incident normally on the face AC.

34) A biconvex lens of glass of refractive index 1·5 having focal length 20 cm is placed in a medium of refractive index 1·65. Find its focal length. What should be the value of the refractive index of the medium in which the lens should be placed so that it acts as a plane sheet of glass?

35)A ray of light incident on an equilateral glass prism propagates parallel to the base line of the prism inside it. Find the angle of incidence of this ray. Given refractive index of material of glass prism is √3 .

36) A concave mirror produces a real and magnified image of an objectkept in front of it. Draw a ray diagram to show the imageformation and use it to derive the mirror equation

(b) A beam of light converges at a point P. Now a lens is placed in thepath of the convergent beam 12 cm from P. At what point does thebeam converge if the lens is

(i) a convex lens of focal length 20 cm,

(ii) a concave lens of focal length 16 cm ?

37a) 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 ?b) Use the mirror equation to show that an object placed between f and 2f of a concavemirror produces a real image beyond 2f.

38) (i) A giant refracting telescope 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 thetelescope ?

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

40) When an object is placed between f and 2f of a concave mirror, would the imageformed be (i) real or virtual and (ii) diminished or magnified ?

41) Why does white light disperse when passed through a glass prism ?

Using lens maker’s formula, show how the focal length of a given lens depends uponthe colour of light incident on it.

42) Define the term ‘critical angle’ for a pair of media.

A point source of monochromatic light ‘S’ is kept at the centre of the bottom of acylinder of radius 15.0 cm. The cylinder contains water (refractive index 4/3) to aheight of 7.0 cm. Draw the ray diagram and calculate the area of water surface throughwhich the light emerges in air.

43).(a) Calculate the distance of an object of height h from a concave mirror of radius ofcurvature 20 cm, so as to obtain a real image of magnification 2. Find thelocation of image also.

(b) Using mirror formula, explain why a convex mirror always produces a virtual image?

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