1. LIGHT : REFLECTION AND REFRACTION

2. LIGHT Light is a form of electromagnetic radiation that causes the sensation of sight. It is an indispensable tool without which we cannot explore the colorful beauty of nature. The blue sky, the rainbow, the red of the sunrise and sunset, the twinkling of stars, the radiance of sparkling diamonds and pearls, and shining color of gems are just some of the natural wonders of light and color.

3. NATURE OF LIGHT Light is an electromagnetic wave. These waves do not require any medium for their propagation. The wavelength of visible light waves is very small, only about 4 x 10-7m to 8 x 10-7m The speed of light wave depends on the nature of the medium through which they pass. The speed of light waves in vacuum is very high, being 3 x 108 m/s.

4. Light provides us means of communication. The fibre-optic cables consisting of many glass fibres transmit hundreds of telephone conversations over long distances.

5. REFLECTION OF LIGHT When light falls on the surface of an object, it may be When light falls on the surface of an object, it may be i) absorbedii) transmitted iii) reflected i) absorbedii) transmitted iii) reflected When light falls on the surface of an object, some of it is sent back. The process of sending back the light rays which fall on the surface of an object, is called reflection of light. When light falls on the surface of an object, some of it is sent back. The process of sending back the light rays which fall on the surface of an object, is called reflection of light.

6. IMAGES An image is formed when the light rays coming from an object meet ( or appear to meet) at a point, after reflection from a mirror ( or refraction from a lens). An image is formed when the light rays coming from an object meet ( or appear to meet) at a point, after reflection from a mirror ( or refraction from a lens). Real Image – If the light rays actually meet after reflection or refraction is called real image. It can be obtained on a screen. Real Image – If the light rays actually meet after reflection or refraction is called real image. It can be obtained on a screen. Virtual Image – If the light rays appear to meet after reflection or refraction, then it is called virtural image. It can’t be obtained on a screen. Virtual Image – If the light rays appear to meet after reflection or refraction, then it is called virtural image. It can’t be obtained on a screen.

7. LAWS OF REFLECTION OF LIGHT FIRST LAW – The angle of incidence (i) is equal to the angle of reflection (r ) SECOND LAW – The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.

8. FORMATION OF IMAGE IN A PLANE MIRROR The characteristics of image formed in a plane mirror are The characteristics of image formed in a plane mirror are i) image is virtual i) image is virtual ii) image is erect ii) image is erect iii) image is of the same size of the object. iv) image is formed as far behind the mirror, as the object is in front of it. iii) image is of the same size of the object. iv) image is formed as far behind the mirror, as the object is in front of it. v) image is laterally inverted. v) image is laterally inverted.

9. SPHERICAL MIRROR A spherical mirror is that mirror whose reflecting surface is the part of a hollow sphere of glass. A spherical mirror is that mirror whose reflecting surface is the part of a hollow sphere of glass. It is of two types : It is of two types : i) concave mirrors i) concave mirrors ii) convex mirrors ii) convex mirrors

10. RULES FOR FORMATION OF IMAGE BY SPHERICAL MIRRORS When an object is placed before a spherical mirror, an image is formed. The image is formed at that point where at least two reflected rays intersect (or appear to intersect). When an object is placed before a spherical mirror, an image is formed. The image is formed at that point where at least two reflected rays intersect (or appear to intersect). Now to find out the position of an image formed by a concave mirror, only two rays light is required. We use those rays whose path is certain, the diagram formed in this way is called as ray diagram. Continued… Now to find out the position of an image formed by a concave mirror, only two rays light is required. We use those rays whose path is certain, the diagram formed in this way is called as ray diagram. Continued…

11. To draw ray diagram, the following rules are used: To draw ray diagram, the following rules are used: i) A ray of light parallel to the principal axis of the mirror, passes through the focus after reflection from the mirror. i) A ray of light parallel to the principal axis of the mirror, passes through the focus after reflection from the mirror. ii) A ray of light passing from the center of curvature of the mirror is reflected back along the same path. ii) A ray of light passing from the center of curvature of the mirror is reflected back along the same path. iii) A ray of light passing through the focus of a concave mirror becomes parallel to the principal axis. iii) A ray of light passing through the focus of a concave mirror becomes parallel to the principal axis.  An image of any point is formed at that point where at least two reflected rays intersect or appear to intersect.

12. IMAGE FORMATION BY CONCAVE MIRROR position of the object Position of the image Size of the image Nature of the image At infinity At the focus F Highly Diminished Real and Inverted Beyond C Between F and C Diminished Real and Inverted At C Same size Real and Inverted Between C and F Beyond C Enlarged Real and Inverted At F At infinity Highly enlarged Real and Inverted Between P and F Behind the mirror Enlarged Virtual and irect

13. IMAGE FORMATION BY CONVEX MIRROR Position of the object Position of the image Size of the image Nature of the image At infinity At the focus F, behind the mirror Highly diminished, point size Virtual and erect Between infinity and the pole of the mirror Between p and F, behind the mirror diminished Virtual and erect

14. NEW CARTESIAN SIGN CONVENTION Height downwards (-ve) Direction of Incident light Incident light (-ve) Direction againstDistance along Incident light (+ve) Height upwards (+ve) Height downwards (-ve) Objects on the left N M P X’ X Y’ Y B’ A’ A B

15. MIRROR FORMULA A B CP M N A’ B’ h h’ F R f v Fig 2.3 u

16. FORMATION OF IMAGE BY CONVEX MIRROR A B M N C E D A’ B’F P

17. We will now obtain a relation between the object-distance (u), the image –distance (v) and the focal length (f) of the spherical mirror having small aperture (much less than the radius of curvature (R). This relation is called Mirror Formula. It remains the same in all types of physical situations, whether the image is real or virtual We will now obtain a relation between the object-distance (u), the image –distance (v) and the focal length (f) of the spherical mirror having small aperture (much less than the radius of curvature (R). This relation is called Mirror Formula. It remains the same in all types of physical situations, whether the image is real or virtual

18. We now derive the mirror formula for a concave mirror producing a real image in fig 2.3. We now derive the mirror formula for a concave mirror producing a real image in fig 2.3. When the object AB is of size or height (h) is placed on the left in front of the concave mirror MN, beyond its centre of curvature C, The image formed is real, inverted and diminished in size (h’) When the object AB is of size or height (h) is placed on the left in front of the concave mirror MN, beyond its centre of curvature C, The image formed is real, inverted and diminished in size (h’)

19. Using the New Cartesian Sign Convention, we have Using the New Cartesian Sign Convention, we have Object distance = PB = - u Object distance = PB = - u Image distance = PB’= -v Image distance = PB’= -v Focal length = PF = -f Focal length = PF = -f Radius of curvature = PC = -R Radius of curvature = PC = -R Now in fig 2.3, the right angle triangles ∆ A’B’P and ∆ ABP, are similar, so that Now in fig 2.3, the right angle triangles ∆ A’B’P and ∆ ABP, are similar, so that A’B’ PB’ -v v A’B’ PB’ -v v AB PB -u u AB PB -u u 3,1

20. Similarly in the right angled triangles, ABC and A’B’C’ are similar, so that Similarly in the right angled triangles, ABC and A’B’C’ are similar, so that A’B’ CB’ A’B’ CB’ AB CB AB CB As we measure all distances from the pole P, we have As we measure all distances from the pole P, we have CB’ = PC – PB’ CB’ = PC – PB’ CB = PB – PC CB = PB – PC Using equation 3.2 we get Using equation 3.2 we get A’B’ PC – PB’ (-R)-(- v) -R + v A’B’ PC – PB’ (-R)-(- v) -R + v AB PB – PC (-u)–(-R) -u + R AB PB – PC (-u)–(-R) -u + R 3.3

21. Comparing Eqs. (3.1) and (3.3), we get Comparing Eqs. (3.1) and (3.3), we get - R + v v - R + v v - u + R u - u + R u Or, uR + vR = 2uv Or, uR + vR = 2uv Dividing both sides by uvR, we get Dividing both sides by uvR, we get 1/v + 1/u = 2/R -------------- (3.4) 1/v + 1/u = 2/R -------------- (3.4) When the object AB is taken at a very large distance ( at infinity), as shown the image is formed at the focus F. Thus, when u =∞, v = f, putting the values in eq 3.4, we get When the object AB is taken at a very large distance ( at infinity), as shown the image is formed at the focus F. Thus, when u =∞, v = f, putting the values in eq 3.4, we get 1/f + 1/∞ = 2 / R or f = R/2 ------ (3.5) 1/f + 1/∞ = 2 / R or f = R/2 ------ (3.5)

22. MAGNIFICATION The ratio between the height of the image produced by the spherical mirror to the height of the object is called linear magnification. The ratio between the height of the image produced by the spherical mirror to the height of the object is called linear magnification. Height of the image Height of the image Linear magnification = -------------------------- Height of the object Height of the objecthi M = ---------= v/u M = ---------= v/uho

23. REFRACTION OF LIGHT AND ITS LAWS the ratio of sine of angle of incidence to the sine of angle of refraction is constant. Thus, angle of incidence I and the angle or refraction r are related as the ratio of sine of angle of incidence to the sine of angle of refraction is constant. Thus, angle of incidence I and the angle or refraction r are related as Sin i ------- = n 21 sin r n 21 is a constant and is called the refractive index of second medium with respect to first medium. It is also known as Snell’s law of refraction. ii) The incident ray, the refracted and the normal at the point of incidence lie in the same plane. ii) The incident ray, the refracted and the normal at the point of incidence lie in the same plane.

24. REFRACTIVE INDEX Ans:- For two media and for a light of a particular color, the ratio of sine of incidence angle and sine of refraction angle is called refractive index of second medium with respect to first. Ans:- For two media and for a light of a particular color, the ratio of sine of incidence angle and sine of refraction angle is called refractive index of second medium with respect to first. Sin i --------------------- = n 21 sin r if motion of light is in reverse direction means from medium 2 to medium 1, refractive index is reversible if motion of light is in reverse direction means from medium 2 to medium 1, refractive index is reversible n 12 = sin r/ sin i = 1/n 21 if velocity of light is v1 in first medium and v2 in second medium, if velocity of light is v1 in first medium and v2 in second medium, n 21 = velocity of light in first medium(v 1 )/ velocity of light in second medium (v 2 ) n 21 = velocity of light in first medium(v 1 )/ velocity of light in second medium (v 2 )

25. Refractive index of water is 4/3 and glass is 3/2 with respect to air. What is refractive of glass with respect to water. Ans;- refractive index of air, n 1 = 1.00 Thus, refractive index of water w.r.t. air, n 21 = n 2 = 4/3 Thus, refractive index of water w.r.t. air, n 21 = n 2 = 4/3 Refractive index of glass w.r.t. air = n 31 = n 3 = 3/2 Refractive index of glass w.r.t. air = n 31 = n 3 = 3/2 Refractive index of glass w.r.t water = n 32 Refractive index of glass w.r.t water = n 32 n 32 = n 31 x n 12 = n 31 / n 21 = n 3 /n 2 = (3/2)/(4/3) = 9/8 = 1.125 n 32 = n 31 x n 12 = n 31 / n 21 = n 3 /n 2 = (3/2)/(4/3) = 9/8 = 1.125

26. RULES FOR IMAGE FORMATION IN SPHERICAL LENSES 1) A ray from the object parallel to the principal axis after refraction passes through the second principal focus F2 ( in a convex lens) or appears to diverge ( in a concave lens) from the first principal focus F1 2) A ray of light passing through the first principal focus ( in a convex lens), or appearing to meet at it ( in a concave lens) emerges parallel to the principal axis after refraction.

27. 3) A ray of light passing through the optical centre of the lens, emerges without any deviation after refraction.

28. IMAGE FORMATION BY CONVEX LENS position of the object Position of the image Size of the image Nature of the image At infinity At the focus F2 Highly Diminished Real and Inverted Beyond 2F1 Between F2 and 2F2 Diminished Real and Inverted At 2F1 At F2 Same size Real and Inverted Between F1 and 2F1 Beyond 2F2 Enlarged Real and Inverted At F1 At infinity Highly enlarged Real and Inverted Between F1 and O On the same side of lens Enlarged Virtual and irect

29. IMAGE FORMATION IN CONVEX LENS CONVEX LENS CONVEX LENS A N M F12F1 B C A B’ A’ F2 O

30. LENS FORMULA N M F12F1 C 2F2 B’ A’ F2 O A B

31. Here object distance = OB = -u Here object distance = OB = -u Image distance = OB’ = v Image distance = OB’ = v Focal length = OF2= f Focal length = OF2= f AB = OC AB = OC ∆ ABO ~ ∆ A’B’O are similar ∆ ABO ~ ∆ A’B’O are similar A’B’/AB = OB’/OB = v/-u ……….eq. –(i) A’B’/AB = OB’/OB = v/-u ……….eq. –(i) Similarly ∆ OCE2 ~ ∆A’B’F2 Similarly ∆ OCE2 ~ ∆A’B’F2 A’B’/OC = F2B’/OF2, As AB = OC, then A’B’/OC = F2B’/OF2, As AB = OC, then A’B’/AB = F2B’/OF2 = ( OB’- OF2)/OF2 = (v-f)/f A’B’/AB = F2B’/OF2 = ( OB’- OF2)/OF2 = (v-f)/f ……..eq. – (ii) ……..eq. – (ii)

32. From eq. (i) & (ii) we get, -v/u = v-f/f From eq. (i) & (ii) we get, -v/u = v-f/f On cross multiplication and dividing both sides by uvf, we get, On cross multiplication and dividing both sides by uvf, we get, 1/v – 1/u = 1/f 1/v – 1/u = 1/f

33. IMAGE FORMATION IN CONCAVE LENS Object is at infinity and the image is at F 1 O F1F1 2F 1

34. When the object is between O and Infinity B A 2F 1 F1F1 A' B’ O

35. Image formation in concave lens Position of the object Position of the image Size of the image Nature of the image At infinity Between infinity and optical centre O of the lens At focus F1 Between focus F1 and optical centre O Highly diminished, point sized Diminished Virtual and erect Virtual and erect.

36. POWER OF A LENS The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it. The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it. The power is defined as the reciprocal of its focal length (f) as The power is defined as the reciprocal of its focal length (f) as P = 1/f P = 1/f The SI unit of power of a lens is dioptre denoted by symbol D. The SI unit of power of a lens is dioptre denoted by symbol D. If f is expressed in metres so that 1 D= 1m -1 If f is expressed in metres so that 1 D= 1m -1

37. Human Eye Retina Retina Pupil Pupil Iris Iris Aqueous humour Aqueous humour Vitreous humour Vitreous humour Cornea Cornea Lens Lens Cilliary muscle Cilliary muscle Suspensory ligament Suspensory ligament Choroid Choroid Blind spot Blind spot Optic nerve Optic nerve fovea fovea Different parts of Human eye are as follows:-

39. SIMPLE MICROSCOPE A simple microscope is a convex lens of short focal length. It is also called magnifying lens. A simple microscope is a convex lens of short focal length. It is also called magnifying lens. The convex lens is held near the object to be magnified, such that it is in between the optical centre and principal focus, but close to principal focus. The convex lens is held near the object to be magnified, such that it is in between the optical centre and principal focus, but close to principal focus. An erect virtual and enlarged image A1B1 is formed at the least distance of distinct vision as shown in fig. Next page. An erect virtual and enlarged image A1B1 is formed at the least distance of distinct vision as shown in fig. Next page.

41. Magnification Size of the image Size of the image M = Size of the object M = Size of the object = Distance of the image from eye = Distance of the image from eye Distance of object from eye Distance of object from eye M = A1B1/AB = D/f ( because eye is held close to lens), Thus, if a convex lens of focal length 6.25 cm is used its magnification is M = A1B1/AB = D/f ( because eye is held close to lens), Thus, if a convex lens of focal length 6.25 cm is used its magnification is m = D/f = 25 cm/ 6.25 cm = 4 m = D/f = 25 cm/ 6.25 cm = 4

42. COMPOUND MICROSCOPE Construction – A compound microscope consists of two metallic tubes such that they can easily slide in one another. Construction – A compound microscope consists of two metallic tubes such that they can easily slide in one another. The tubes are blackened from inside to prevent any internal reflection. The tubes are blackened from inside to prevent any internal reflection. On the side of the smaller tube a convex lens of very small focal length called objective lens is fitted which faces towards the object. On the side of the smaller tube a convex lens of very small focal length called objective lens is fitted which faces towards the object.

44. On the side of bigger tube, another convex lens of larger focal length is fitted. This lens is called eye lens. On the side of bigger tube, another convex lens of larger focal length is fitted. This lens is called eye lens. Working – A tiny object AB is placed in between F0 and 2F0 of the objective lens, when it forms a real, inverted and magnified image A1B1 on the other side of objective lens, i.e. within the tubes. Working – A tiny object AB is placed in between F0 and 2F0 of the objective lens, when it forms a real, inverted and magnified image A1B1 on the other side of objective lens, i.e. within the tubes.

45. Now the eye lens tube is moved backward or forward, such that the real image A1B1 falls between the principal focus (Fe) and its optical centre (O) of the eye lens. Now the eye lens tube is moved backward or forward, such that the real image A1B1 falls between the principal focus (Fe) and its optical centre (O) of the eye lens. The rays starting from the real image A1B1 on passing through the eye lens give rise to a divergent beam of light. The rays starting from the real image A1B1 on passing through the eye lens give rise to a divergent beam of light. When these divergent rays are received by the eye, they appear to come from the points A2 and B2. When these divergent rays are received by the eye, they appear to come from the points A2 and B2. Thus A2B2 is the virtual, but highly enlarged image of the object AB. Thus A2B2 is the virtual, but highly enlarged image of the object AB.

46. The image formed here is inverted with respect to the object. The image formed here is inverted with respect to the object. However, this does not make any difference as most of the biological specimens seen under the microscope are round and oval or not very well defined in shape. However, this does not make any difference as most of the biological specimens seen under the microscope are round and oval or not very well defined in shape.

47. magnification The magnifying power of a compound microscope is the ratio between the final size of the virtual image to the actual size of the object. The magnifying power of a compound microscope is the ratio between the final size of the virtual image to the actual size of the object. M = (D x L) where D = least distance of M = (D x L) where D = least distance of F0 x fe distinct vision, L= tube length, f0 = focal length of objective, F0 x fe distinct vision, L= tube length, f0 = focal length of objective, fe = focal length of eyepiece. fe = focal length of eyepiece.

48. ASTRONOMICAL TELESCOPE Astronomical telescope is an optical device used to for seeing heavenly bodies such as the stars, the Sun, the Moon, etc, closely. Astronomical telescope is an optical device used to for seeing heavenly bodies such as the stars, the Sun, the Moon, etc, closely. Construction – It consists of two convex lenses, i.e. an objective lens of very large focal length and eye lens of very small focal length. Construction – It consists of two convex lenses, i.e. an objective lens of very large focal length and eye lens of very small focal length. The two lenses are mounted on separate tubes which can slide in one another. The two lenses are mounted on separate tubes which can slide in one another.

50. working The rays coming from a distant heavenly body are parallel to one another, but generally not parallel to the principal axis. The rays coming from a distant heavenly body are parallel to one another, but generally not parallel to the principal axis. These rays, on passing through the objective lens, suffer refraction and hence, converge in the plane of the principal focus to form a real, inverted and diminished image AB of a distant body. These rays, on passing through the objective lens, suffer refraction and hence, converge in the plane of the principal focus to form a real, inverted and diminished image AB of a distant body.

51. Now the eye lens tube is moved backward or forward so that the real image AB falls within the principal focus (fe) and the optical centre(O) of the eye lens. Now the eye lens tube is moved backward or forward so that the real image AB falls within the principal focus (fe) and the optical centre(O) of the eye lens. The rays starting from the real image AB on passing through the eye lens give rise to a divergent beam of light. The rays starting from the real image AB on passing through the eye lens give rise to a divergent beam of light. When this divergent beam reaches the eye to it the rays appear to come from A1B1. Thus, A1B1 is the final virtual and enlarged image formed. When this divergent beam reaches the eye to it the rays appear to come from A1B1. Thus, A1B1 is the final virtual and enlarged image formed.

52. Magnification The ratio between the angle subtended by the final image on the eye to the angle subtended by the object on the unaided eye is called the magnifying power of telescope. The ratio between the angle subtended by the final image on the eye to the angle subtended by the object on the unaided eye is called the magnifying power of telescope. m = fo/fe, fo – focal length of objective m = fo/fe, fo – focal length of objective fe – focal length of eye lens fe – focal length of eye lens

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