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Hello dude !

You should use the following books for Mthematics Olymipad :

GEOMETRY

PROBLEM BOOKS

S. L. Greitzer International Mathematical Olympiad 1959-1977, MAA.

M. S. Klamkin International Mathematical Olympiad 1978-1985, MAA.

C. R. Pranesachar, S. A. Shirali, B. J. Venkatachala, and C. S. Yogananda Mathematical Challenges from the Olympiads Interline publishing, Bangalore. (Contains problems and solutions of International Mathematical Olympiad from 1986-1994).

Durrel M. A., Modern Geometry Macmillan & Co., London.

H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited Mathematical Association of America.

S. L. Loney, Plane Trigonometry Macmillan & Co., London.

NUMBER THEORY

I. Niven & H. S. Zuckerman An Introduction to the Theory of Numbers Wiley Eastern Ltd. New Delhi.

David Burton Elementary Number Theory Universal Book Stall, New Delhi.

G. H. Hardy & Wright An introduction to the theory of numbers, Oxford University Publishers.

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Ya i also found same things. Admin should take action against it.

THANKS RANJANA.............

plzzzzz explain how to learn?

I want all the answer....

very nice yaar...........

1. Determine the speed of light in glass which has refractive index of 1.5, if the speed of light in vacuum is 3x10⁸m/s.

2. A 1cm high image is obtained on a screen a t a distance of 20cm from a convex lens of focal length 10cm.What is the size the object?

3. The radius of curvature of a convex mirror is used on a moving automobile is 2.0 m. A truck is coming behind it at a constant distance of 3.5 m. Calculate (1) the position, and (2) the size of image relative to the size of the truck. What will be the nature of the image?

4. (a) Draw a ray diagram to show passage of two rays of light through a rectangular slab of glass, when the angle of incidence is zero in one case and a littler less than 90⁰ in the other case.

5. A transparent medium A floats on another transparent medium B .When a ray of light travels obliquely from A into B the reflected ray bends away from the normal. Which of the media A and B is optically denser and why?

THANKS

Comments Plzzzzzzzzzzzzzz

LIGHT –REFLECTION AND REFRACTION

QUESTIONS TO PRACTICE

1. What are the differences between real image and virtual image?

2. The radius of curvature of a concave mirror is -46cm.What is its focal length?

3. How will you identify a plane mirror, a concave mirror and a convex mirror without touching their surface?

4. Which mirror has a wider field of view? Why?

5. What happens to a ray of light when it travels from a rarer medium to a denser medium?

6. What will be the signs of u, v and f for a convex lens as per sign convention?

7. State Snell’s law of refraction?

8. A lens always forms a diminished, erect and virtual image .Identify the nature of the lens?

9. Where should an object be placed so that a real and inverted image of the same size is formed using a convex lens?

10. How is the power of a lens related to its focal length?

11. What is the S I unit of power of a lens? Define.

12. Two lenses having power P1 and P2 are placed in contact. What is the net power of the combination?

13. Two lenses of powers 4D and -5D are kept in contact. Find the focal length of the combination. What is the nature of the combination?

14. What do you understand by the term refractive index?

15. The image of our face is viewed in and out of the curved surface of a spoon. What change in the image is observed? How will you explain this?

16. You should not look at the sun directly or even into a mirror reflecting the light from the sun. Justify.

17. You need an erect and enlarged image of on object on a mirror. Which mirror would you choose?

18. You need to get an image of the size as that of the object using a lens. What is the suitable lens to be used?

19. The image of an object at a distance of 20 cm from a mirror is formed at the object itself.

1) Identify the mirror 2) The nature of the image

3) size of the image 4) the focal length of the mirror

5) radius of curvature of the mirror

Draw the corresponding ray diagram.

20. Draw a ray diagram to show the formation of the image of an object placed at the centre of curvature of a concave mirror.

21. A convex mirror used on an automobile has radius of curvature of 2 m .If a car is located at 4 m from the mirror, find the position nature and size of the image

22. Why is convex mirror preferred to be used as a driver’s rear-view mirror?

23. For what position of an object, a virtual image is formed by a convex lens? Draw a ray diagram to show the formation of a virtual image by a convex lens. What are the other characteristics of the image?

24. Why is a concave lens is called diverging lens, whereas a convex lens a converging lens? Explain with the help of ray diagrams.

25. Why the apparent depth of a swimming pool is less than its real depth? On what factors does the difference between the two depend?

26. Two lenses having power of 2.0D and 0.25D are combined together. What is the

(a) net power of combination?

(b) focal length of the combination?

27. Give two uses of convex lens.

28. Give two uses of convex mirrors

29. Give two uses of concave mirror.

30. Give two uses of concave lens

31. Give two uses of plane mirror.

32. Show the path of a ray of light through a rectangular glass slab. Label incident ray, refracted ray, emergent ray, the angle of incidence and angle of emergence and lateral displacement. Why is angle of incidence equal to the angle of emergence?

33. Drawing ray diagrams for an object at infinity and by using the new sign convention show that the focal length of a concave mirror is negative and that of convex mirror is positive.

34. State three rules for drawing geometric images in concave lens.

28. A reflected ray of light makes an angle of 90⁰ with the incident ray of light. What are the angle of incidence and the angle of reflection? Draw a diagram to illustrate these rays.

29. State the laws of refraction.

30. An object 4cm high is placed 15cm away from a concave lens of focal length 10cm. Draw a ray diagram and find the position, size and nature of the image formed.

35. An object is kept in front of a concave mirror of focal length 20cm.The image formed is three times the size of the object. Calculate the two possible distances of the object from the mirror.

36. An object 0.4m high is placed at a distance of 0.8m from a concave mirror of radius curvature 0.4m. Find the position, nature and size of the image formed?

37. Two thin converging lenses of focal length 15cm and 30cm are held in contact with each other. Calculate the power and focal length of combination.

38. Find the position of an object which when placed in front of a concave mirror of focal length 20cm, produces a virtual image, which is twice the size of the object.

39. Draw a ray diagram to show the formation of an object placed between the pole and focus of a concave mirror.

40. What is a lens? Distinguish between a convex and concave lens.

41. What do you understand by the power of a lens? Define magnification in case of spherical mirror and lens. Mention the new Cartesian sign convention applicable to in this case.

42. Draw a ray diagram to show the formation of the image of an object placed between optical centre and focus of a convex lens.

43. You are required to obtain an erect image of an object placed in front of a concave mirror of focal length 15cm.What should be the approximate distance of the object from the pole of the mirror? What is the nature of the image? Is the image larger of smaller in size than the object? Draw a ray diagram to show the formation of image.

44. An object of size 5cm is placed at a distance of 25cm from the pole of a concave mirror of radius of curvature 30cm.Calculate the distance and size of the image so formed. What will be the nature of the image?

45. An object of size 3cm is placed at a distance of 15cm from a convex lens of focal length 10cm.Calculate the distance and size of the image so formed. What will be the nature of the image?

46. Determine the speed of light in glass which has refractive index of 1.5, if the speed of light in vacuum is 3x10⁸m/s.

47. A 1cm high image is obtained on a screen a t a distance of 20cm from a convex lens of focal length 10cm.What is the size the object?

48. The radius of curvature of a convex mirror is used on a moving automobile is 2.0 m. A truck is coming behind it at a constant distance of 3.5 m. Calculate (1) the position, and (2) the size of image relative to the size of the truck. What will be the nature of the image?

49. (a) Draw a ray diagram to show passage of two rays of light through a rectangular slab of glass, when the angle of incidence is zero in one case and a littler less than 90⁰ in the other case.

50. A transparent medium A floats on another transparent medium B .When a ray of light travels obliquely from A into B the reflected ray bends away from the normal. Which of the media A and B is optically denser and why?

51. Where will the image is formed by a convex mirror if the object is placed between infinity and the pole of the mirror?

52. A convex lens has a focal length of 50cm. Calculate its power.

53. IDENTIFY THE LENS/MIRROR

i) Focal length positive

ii) Focal length negative

iii) Power positive

iv) Power negative

v) Forms virtual image always magnified

vi) Forms only diminished virtual images

vii) Magnification always positive

viii) Magnification always less than one

ix) Can produce image of the same size

x) Forms real point sized image

xi) Forms virtual point sized image

xii) Used as shaving mirror

xiii) Used as rear view mirror

xiv) Have wide field of view

xv) Converges the incident rays

xvi) Diverges the incident rays

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NCERT Textbook

(a) Myopia

Myopia is also known as near-sightedness. A person with myopia …………………. This defect may arise due to excessive curvature of the eye lens, or (ii) elongation of the eyeball.

(b) Hypermetropia

Hypermetropia is also known as far-sightedness… …………………….. This defect arises either because (i) the focal length of the eye lens is too long, or (ii) the eyeball has become too small.

Correction

Myopia and hypermetropia are due to problems associated with cornea. It doesn’t have much to do with eye lens.

NCERT Textbook

This defect is called Presbyopia. It arises due to the gradual weakening of the ciliary muscles and diminishing flexibility of the eye lens. Sometimes, a person may suffer from both myopia and hypermetropia. Such people often require bi-focal lenses.

Correction

Presbyopia is often confused as the existence of myopia and hypermetropia together but a close examination of the cause of hypermetropia and myopia would assure you that they cannot occur together. Presbiopia is a problem associated with ciliary muscle and eye lens.

NCERT Textbook

……..This is called Ohm’s law. Inother words –

V α I

or V/I = constant= R

or V=IR

Correction

V = IR is an equation which is derived from the mathematical definition of resistance in DC circuits R = V / I . This is true in every conductor ohmic or non-ohmic. Ohm’s law actually says that the resistance is independent of the applied voltage and hence R is a constant.

So V / I is a constant

And V α I.

NCERT Textbook

Correction

The power of cornea is around 43 Dioptres whereas the power of eye lens is 15 Dioptres. The diagrams shown below as in the NCERT textbook show that the maximum deviation is occurring at eye lens which is grossly misleading.

Misconceptions about light

1. A plane mirror does not form an inverted image

A plane mirror can form an inverted image when the plane of the object is perpendicular to the plane of the mirror.

For example, consider a line object with end points A and B in front of a plane mirror as shown.

If we just concentrate at the end points, as we usually do in drawing ray diagrams, we see that A should be as far behind the mirror as it is in front of it and so for B. So it is obvious that the image is inverted.

2. Plane mirrors never form real images

Plane mirror may form a real image when converging rays from an optical device fall on it.

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