Short Notes: REFRACTION

What is Refraction?

  • The change of direction of light because of change of medium is known as Refraction or Refraction of Light.
  • This change occurs because of difference in speed of light in different media.

Principle:  The light travels at faster speed in rare medium and at slower speed in denser medium.

  • rarer to denser medium ———->  Light moves towards the normal
  • Denser to rarer medium  ———> Light moves away from the normal
  • Ray emerging after the denser medium goes in the same direction and parallel to the incident ray.

Refraction through a rectangular glass slab

  • Here in this figure AO is the light ray travelling in air and incident on glass slab at point O.
  • Now on entering the glass medium this ray bends towards the normal NN’ that is light ray AO gets refracted on entering the glass medium.
  • After getting refracted this ray now travels through the glass slab and at point B it comes out of the glass slab as shown in the figure.
  • Since ray OB goes from glass medium to air it again gets refracted and bends away from normal N1N’1 and goes in direction BC.
  • Here AO is the incident ray and BC is the emergent ray and they both are parallel to each other and OB is the refracted ray.
  • Emergent ray is parallel to incident ray because the extent of bending of the ray of light at the opposite parallel faces which are PQ (air-glass interface) and SR (glass-air interface) of the rectangular glass slab is equal and opposite.
  • In the figure i is the angle of incidence, r is the angle of refraction and e is the angle of emergence.
  • Angle of incidence and angle of emergence are equal as emergent ray and incident ray are parallel to each other.
  • When a light ray is incident normally to the interface of two media then there is no bending of light ray and it goes straight through the medium.

Laws of refraction of light

Till now we have seen that refraction is due to change in the speed of light as it enters from one transparent medium to another. Further, experiments have shown that refraction of light occurs according to certain laws, which are as following:

  1. The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
  2.  The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media. This law is also known as Snell’s law of refraction.

When i is the angle of incidence and r is the angle of refraction then

Note:  the constant value, n , is called as the refractive index of the second medium with respect to the first.

The Refractive Index

  • Refractive index is the relative speed of propagation of light in different media as light propagates with different speeds in different media.
  • Let v1 be the speed of light in medium 1 and v2 be the speed of light in medium 2 then the refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. So,

  • Similarly you can work out for the refractive index of medium 1 with respect to medium 2.
  • Note:  Use the formula mentioned below when one of the media is air, take the speed as speed of light in vacuum, here, taken as a constant c.

 

Refraction by Spherical Lenses

  • A lens is a piece of transparent glass bound by two spherical surfaces.
  • There are two types of lens

A convex lens bulges outward and is thick at the center and thinner at the edges. Convex lens converges the light rays as shown below in the figure 1(a).

Hence convex lenses are called converging lenses.

A concave lens bulges inward and is thinner in the middle and thicker at the edges. Such lenses diverge light rays as shown in Figure 1(b)

Such lenses are called diverging lenses.

Image Formation by Lenses

  • Image formation by a convex lens for different positions of the object is shown below in the table
Position of the object

 

Position of the image Relative size of the image Nature of the image
Infinity At focus F2 Highly diminished, point sized Real and inverted
Beyond 2F1 Between F2 and 2F2 Diminished Real and inverted
At 2F1 At 2F2 Same size Real and inverted
Between F1 and 2F1 Beyond 2F2 Enlarged Real and inverted
At focus 2F1 At infinity Infinitely large or highly enlarged Real and inverted
Between F1 and optical center O On the same side of the lens as the object Enlarged Virtual and erect

 

  • Nature, position and relative size of the image formed by a concave lens for various positions of the object is given below in the table
Position of the object

 

Position of the image Relative size of the image Nature of the image
At infinity At focus F Highly diminished, point-sized Virtual and erect
Between infinity and optical center O of the lens Between F1 and optical center O Diminished Virtual and erect
  • Note: A concave lens will always give a virtual, erect and diminished image, irrespective of the position of the object.

Image Formation in Lenses Using Ray Diagrams

  1. CONVEX LENS

2. CONCAVE LENS

Sign Convention for Spherical Lenses

  1. All the distances are measured from the optical center of the lens.
  2. The distances measured in the same direction as that of incident light are taken as positive.
  3. The distances measured against the direction of incident light are taken as negative.
  4. The distances measured upward and perpendicular to the principle axis are taken as positive.
  5. The distances measured downwards and perpendicular to principle axis is taken as negative.

Lens Formula and Magnification

  • Lens Formula gives the relationship between object distance (u), image image-distance (v) and the focal length (f ) and is expressed as:

  • The magnification produced by a lens is defined as the ratio of the height of the image and the height of the object.

  • Magnification produced by a lens is also related to the object-distance u, and the image-distance v and is given by

  • The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by

  • Power of a convex lens is positive and that of a concave lens is negative.
  • The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D.
  • 1 dioptre is the power of a lens whose focal length is 1 meter so, 1D=1m–1.

Keep practicing…

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