Chapter 10(part 2)

REFLECTION AND REFRACTION OF LIGHT

CONTENT

  1. REFRACTION OF LIGHT
  2. REFRACTION THROUGH A RECTANGULAR GLASS SLAB
  3. REFRACTIVE INDEX
  4. REFRACTION THROUGH SPHERICAL LENSES
  5. IMAGE FORMATION BY LENSES
  6. SIGN CONVENTION FOR SPHERICAL LENSES
  7. LENS FORMULA AND MAGNIFICATION
  8. POWER OF A LENS
  9.  DIFFERENCE BETWEEN REFLECTION AND REFRACTION
  10. TEST FOR PRACTICE

Refraction of light:

  • When a light ray travels from one transparent medium to another transparent medium, it changes its path in the second transparent medium. This phenomenon of light is called as Refraction of light.
  • Examples of Refraction – i) bending/displacement of pencil, partly immersed in water (see pic 10.15). ii)  Raising of bottom of a tank or pond containing water. iii) the letters appear raised when viewed through the glass slab.
  • In refraction of light, the light changes its direction of propagation in the second medium.  
PIC 10.15

Terms associated with Refraction:

pic 10.16
  • Incident ray:  The ray that incidence or falls upon a surface is called as incident ray. (in pic 10.16 PQ is incident ray)
  • Refracted ray: The ray that moves in the second medium after refraction is called as refracted ray. (in pic 10.16 RS is refracted ray )
  • Emergent ray: If the light ray suffers two reflection that means if the light ray passes through the second medium and emerge to the first medium (as shown in pic 10.17) then the ray that emerged in the second medium is called as emergent ray. ( in pic 10.17 GH is the emergent ray)
  • Interface of two media : The boundary or the end line of the first medium and the starting line of the second medium is a certain and also a unique line (or plane)  for the two medium. This is known as the interface of two media. ( in pic 10.16 AB is the interface of media air and glass)
  • Angle of incidence : The angle made by the incident ray with the normal to the interface of two media at the point of incidence is called as angle of incidence. It is denoted as “i”.
  • Angle of refraction : The angle made by the refracted ray  with the normal to the interface of two media at the point of incidence is called as the angle of refraction. It is denoted as “r”.

Laws of Refraction :

   There are two laws of reflection.

  1. The incidence ray, the refracted ray and  the normal to the interface of two transparent media at the point of incidence ,all lie in one plane.
  2. The ratio of sine of angle of incidence and sine of angle of refraction is a constant, for the light of a given colour and for two given pair of media. This law is also known as Snell’s law of refraction.(this true for angle 00 < i <900 )

Refraction through a Rectangular glass slab :

  • When a light ray falls obliquely in a rectangular glass slab then it refracted two times as shown in pic 10.17. In the figure the light ray enters into the glass slab in point O and  O. At this two points the light ray is refracted. Because in these two points the light ray moves from one medium to another medium.
  • At the point O the light ray moves from Air medium to the glass medium and moves in the glass medium till the point O. Then at the  point O it again changes its way from glass medium to the air medium. The points O and O lies on the interface of transparent media pair Air-glass and glass-air respectively. (See pic 10.17)
Pic 10.17

You can see that the incidence ray EO and the emergent ray OH are parallel. You can also notice that the light ray has bent towards the normal NN at the point O and it also has bent away from the normal MM’ at point O’.

  • If the light ray falls normal to the interface of two media then the direction of the light ray does not change its direction in the second media after refraction. That means if the angle of incidence is 00 then the angle of refraction is also 00.
  • In this case the incident ray (EF) and the emergent ray (GH) are parallel to each other.

Refractive index:

  • Refractive index is defined as the relative speed propagation of light in different media. It may be expressed as the extent of the change in direction that takes place in a given pair of media.
  • The constant in the Snell’s law is defined as the refractive index of 2nd medium with respect to the 1st medium.  
  • Hence by Snell’s law if the given pair of medium is changed then the refractive index is changed. Because in Snell’s law it is given that the ratio of sine of incidence angle and refraction angle is constant for two given media.
  • Refractive index of different mediums is different.

Why different medium has different refractive index:

  • Refractive index of any medium have a relation with  the speed of propagation of light in that medium
  • The speed of propagation of light is 3×108 m/s in vacuum, which is the highest speed of propagation of light in any medium. The speed of propagation of light in air medium is slightly smaller than the speed of light in vacuum medium. Hence the speed of light in vacuum medium and air medium are considered as equal.
  • In any other medium the speed of light decreases then the speed propagation of light in vacuum or air medium.

Refractive Index of two given pair of media

  • If a light ray travels from medium 1 to medium 2 then (see pic 10.18) the refractive index of medium 2 to with respect to the medium 1 is represented by symbol “n21.
  • As there is a relation between the refractive index of medium and the speed of propagation of light in that media, we can express the refractive index of a medium as the relative speed of propagation of light.
Pic 10.18

If the speed of light in the first medium is v1 and the speed of light in  the 2nd medium is v2 then the refractive  index of the second medium with respect to the 1st medium is expressed in terms of equation as

  • Likewise the refractive index of the 1st medium with respect to the 2nd medium is noted as n12 and expressed as
  • If the 1st medium is vacuum or air, then the refractive index of medium 2 with respect to the medium 1 i.e with respect to vacuum or air is called as absolute refractive index of the 2nd medium.
  • Hence the absolute refractive index of any medium is defined as the ratio of speed of light in vacuum and speed of light in that medium. It is denoted as n2 or nm.

Generally the speed of light in vacuum is denoted as “c” and “v” is the speed of light in the given medium then

  • This absolute refractive index of any medium is also called as refractive index of that medium. Hence the refractive index of a medium is defined as the ration of speed of light in vacuum or air to the ratio of the speed of light in that medium.
  • Examples: the refractive index of vacuum is 1,the refractive index of air is 1.003 (considered as 1), the refractive index of water is 1.33.
  • The refractive index of water denoted as “nw” and its value is 1.33. It means that the ratio of speed of light in vacuum or air to the speed of light in water is equal to 1.33.
  • Refractive index has no unit or it is unitless.

Optical density and Mass density:

  1. Mass density: It is defined as the amount of substance present per unit volume. Mathematically,
  2. Optical density: The ability of a medium to refract light is called as optical density.
  3. According to optical density the media are classified in Two types. i) optically denser medium  ii) optically rare medium
  4. Optically denser medium: In comparing two media, the medium with the larger refractive index is called as optically denser medium then the other.
  5. The medium among two media, in which the speed of light is smaller, is called as optical denser medium than the other.
  6. Optically rear medium:  In comparing two media, the medium with the smaller refractive index is called as optically rear medium.
  7. The medium among two media, in which the speed of light is greater, is called as optical rear medium than the other.
  8. Example: the refractive index of kerosene is 1.44 and refractive index of water is 1.33.hence the kerosene is optically denser then water. But kerosene is optically rear than crown glass whose refractive index is 1.52.
  9. An optically denser medium may not possess a greater mass density. For example kerosene is optically denser than water but its mass density is less than water.
  10.  When a light ray travels from rear medium to denser medium it bends towards the normal, as it slows down in the denser medium.
  11. Ex: in pic 10.17, when the ray enters to the glass (denser medium) from the air medium ( rear medium) it bends towards the normal NN’.
  12. When a light ray travels from denser to rear medium it bends away from the normal, as it speeds up in the rear medium.

Ex: In pic 10.17, when the ray comes out from the glass (denser medium) to the air medium ( rear medium) it bends away from the normal MM’.

Refraction by Spherical lenses:

Spherical lenses:

  •  A transparent material bound by two surface, of which one or both surfaces are spherical, is called as spherical lens.
  • A lens is bound by at least one spherical surface. The lens which has one spherical surface, the other surface of that lens is plane.
  • The spherical lenses are TWO types. i) convex lens  ii) concave lens

Convex lens:

  • The spherical lens in which the spherical surface is bulging outwards, is called as convex lens. (See pic 10.19 a)
  • If there are two spherical surfaces and the two surfaces are bulging outwards of a lens, then it is called as double convex lens.
  • It is thicker at the middle as compared to the edges.

All the parallel rays those fall on the refracting surface of a convex lens after refraction converged at one point. Hence it is called as converging lens.

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Concave lens :

  • The spherical lens in which the spherical surfaces are curved inwards are called as concave lens. ( see pic 10.19 b )
  • If there are two spherical surfaces and the two surfaces are curved inwards of a lens, then it is called as double concave lens.
  • It is thicker at the edges than the middle.
  • All the parallel rays those fall on the refracting surface of a concave lens after refraction seems to be diverged from one point. Hence it is called as diverging lens.

Some terms associated with spherical mirror:

  •  Center of curvature: The surfaces of  a spherical lens are the parts of a sphere. The center of this sphere is called as the center of curvature of that spherical lens.
  • It is denoted as “C”.
  • As, in a double convex or in a double concave lens there are two spherical surfaces, hence there are two center of curvature. These are denoted as “C1” and “C2”.
  • Also it is generally denoted as 2F1 and 2F2.(see pic 10.19)
  • Principal axis of lens: The imaginary straight line that joins the two center of curvature of a lens is called as the principal axis of the lens.
  • The imaginary line that passes through the C1 and C2 (in the pic 10.19) is called as the principal axis of the lens.
  • Optical Center: The central point of lens is called as the optical center of the lens and it is denoted as “O”.
  • A ray that passes through the optical center of a lens suffers no deviation.
  • Aperture of lens: The effective diameter of the circular outline of spherical lens is called as its aperture.
  • Focus: The definition of focal length is different for concave and convex lens.
  • Focus of convex lens: All the rays those fall parallel to the principal axis of a convex lens after refraction converged at one point on the principal axis. This is called as focal length of the convex lens.
  • As there are two refracting surface of a convex lens hence there are two focus of a convex lens.
  • The focus point is denoted as F. hence as there are to foci, these are denoted as F1 and F2.
  • Focus of Concave lens: All the rays those fall parallel to the principal axis of a concave lens after refraction seems to be diverged from one point on the principal axis. This point of a concave lens is called as the principal focus.
  • As there are two refracting surface of a concave lens hence there are two focus of concave lens.
  • The focus point is denoted as F. hence as there are to foci, these are denoted as F1 and F2.
  • Focal length of the spherical lens: The distance from the optical center (O) to the principal focus (F) of a spherical lens (both in concave and convex lens) is called as the focal length of the spherical lens. 
  • It is denoted by “f”.

Image formation by Lenses:

     Golden Rules of image formation by ray diagram in spherical lenses:

1.If a ray of light falls parallel to the principal axis of a convex lens then after refraction it passes through the principal focus on the other side of the convex lens. But in concave lens the ray that falls parallel to the principal axis, after refraction appears to diverge from the principal focus located on the same side of the lens.(see pic 10.20)

Pic 10.20

2.If a ray of light passes through the focus of a convex lens then after refraction it will emerge parallel to the principal axis.(see pic 10.21 a). But in case of concave lens if a ray of light Appears to meet at the principal focus of a concave lens, after refraction it emerges parallel to the principal axis.( see pic 10.21 b)

3.If a ray of light passes through the optical center of lens then it suffers no deviation. It means the ray emerges without any deviation. This rule is same for both convex and concave lens.( see pic 10.21 below a & b)

Pic 10.21

Q3. Among the rules of the mirror formation by ray diagram in spherical lens, which law is same for both concave and convex lenses ?

Ans: the rule that same for both convex and concave lenses is – If a ray of light passes through the optical center of lens then it suffers no deviation. It means the ray emerges without any deviation.

Image formation by convex lens by ray diagram:

  1. There are six cases for formation of image in a convex lens .These are noted below.

   Case 1 :-

Position of the object at infinity (see pic 10.22 a)

  • Always parallel rays come from a object at infinity. As per golden rule (i) the refracted rays pass through the focus as seen in pic 10.22.
  • Hence the position of image is at focus at the other side of the lens (F2). As the two refracted rays meet each other at that point.
  • The size of the image is “highly diminished or point size and nature of the image is “Real and inverted”.
  Pic 10.22

Case 2:-

Position of the object – near the Center of Curvature (C1 or 2F1) (see pic 10.23 )

  • We are free to choose any two rays to construct the ray diagrams. But for making it easy We always take an incident ray parallel to the principal axis and another incident ray passes through the nearest point of the object .
  • Hence, by drawing the ray diagram we get the position of the image is “between F2 and 2F2and nature of the image is “real and inverted.” And the size of the image is diminished.
pic. 10.23

Case 3:- (see pic 10.24)

Position of the objectat the center of curvature or 2F1

Position of the image at 2F2

Nature of the image real and inverted

size of the image same as the object

pic. 10.24

Case 4:- (see pic 10.25 )

Position of the objectbetween2F1 and F1

Position of the image beyond 2F2

Nature of the image real and inverted

size of the image enlarged

pic. 10.25

Case 5:- (see pic 10.26)

Position of the objectat principal focus F1

Position of the image – at infinity

Nature of the image-  real and inverted

size of the image- highly enlarged or infinitely large

pic. 10.26

Case 6:- (see pic 10.27)

Position of the object- between focus F1 and a optical center O

Position of the image- as the same side of the lens as the object

Nature of the image- virtual and erect

size of the image–  enlarged

pic. 10.27

B) In concave lens :-In case of concave lens there are only two positions of object.

   Case 1 :-[pic 10.28 a]

Position of the object at infinity

Position of the image- at focus F1

Nature of the image- virtual and erect

size of the image–  highly diminished or point sized

Pic. 10.28 a

   Case 2 :- (pic 10.28 b)

Position of the object between infinity and optical center O

Position of the image- between F1 and O

Nature of the image- virtual and erect

size of the image- diminished

Pic. 10.28 b

sign convention for spherical lens:

  •  All the distances from a spherical lens are measured from the optical center O. Hence, here the optical center O is considered as the origin.
  •  All the distances at the left hand side of the origin (optical center) is taken as –ve. While the distances at the right hand side of the spherical mirror are taken as +ve.
  •  All the heights those are above the principal axis are taken as +ve and the heights below the principal axis are taken as –ve.
  •  The focal length of the convex lens is always taken as +ve, while the focal length of the concave length is taken as –ve.
  • In concave lens both the object distance and the image distance are always taken as -ve. Because the object is always at the left hand side of  the optical center (O) and the image also formed at the left hand side of the optical center (O).

Lens formula:

  • The relation between the object distance u, image distance v, and the focal length f of a spherical lens is known as the lens formula
  • Mathematically,
  • This lens formula is general, means it is valid for all situations for any spherical lens.

Magnification:

  • It is defined as the ratio of the image height produced in a spherical lens to that of object height.
  • It is represented by the letter m.
  • If h is the height of the object and h’ is the height of the image given by a lens, then the magnification produced by the lens is given by,  
  • The magnification is also related to the image distance v and object distance u. mathematically,
  • If the sign of the magnification is +ve, then the image formed is virtual and erect.
  • If the sign of the magnification is –ve, then the image formed is real and inverted.

Power of lens:

  • The degree of convergence or divergence of light ray achieved by a lens is called as the power of that lens. It is denoted as P.
  • The power of the lens is related to the focal length of the spherical lens. Mathematically, the relation can be expressed as,  .
  • Thus the power of lens is inversely proportional to the focal length of that lens. Hence a convex lens of very short focal length, bends the light rays through large angle, by focusing them closer to the optical center. And a concave lens of short focal length diverge the light rays more than the one with longer wavelength.
  •  The S.I. unit of power of lens is “DIOPTRE”. It is denoted as D.
  • If f or focal length is expressed in meter than the power of lens is expressed in dioptre.
  • Hence 1 dioptre is the power of a lens whose focal length is 1m. 1D = 1m-1.
  • The power of convex lens is always +ve, as its focal length is taken as +ve. And the power of concave lens is taken as –ve, as its focal length is taken as negative.
  • Use of lens:

Opticians prescribe corrective lenses indicating their powers. Let us say the lens prescribed has power equal to + 2.0 D. This means the lens prescribed is convex. The focal length of the lens is +0.50m. Similarly, a lens of power – 2.5 D has a focal length of -0.40 m. The lens is concave.

Combination of lens:

  •  The use of more than one lens at a time is considered as combination of lens. They are combined to increase the magnification and sharpness of an object.
  • The net power (P) of the lenses placed
    in contact is given by the algebraic sum of the individual powers P1, P2, P3, … .i.e P1+P2+P3=P
  • The use of powers, instead of focal lengths, for lenses is quite convenient for opticians.
  • During eye-testing, an optician puts several different combinations of corrective lenses of known power, in contact, inside the testing spectacles’ frame. The optician calculates
    the power of the lens required by simple algebraic addition.
  • For example, a combination
    of two lenses of power + 2.0 D and + 0.25 D is equivalent to a single lens of power + 2.25 D.
  • The simple additive property of the powers of lenses can be used to design lens systems to minimize certain defects in images produced by a single lens.
  • Such a lens system, consisting of several lenses, in contact, is commonly used in the design of lenses of
    camera, microscopes and telescopes.
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