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Critical Angle and Total Internal Reflection

Let XY be a surface that separates a denser medium from a rarer medium. OP0 is a ray of light (from the object O in the denser medium) incident obliquely on the refracting surface XY. P0Q0 is the refracted ray. As we increase the angle of incidence i, the angle of refraction also increases. At a certain stage the refracted ray lies along the surface of separation of the two media, i.e., the angle of refraction becomes 90°. The corresponding angle of incidence is called the critical angle (C). The critical angle (C) for a pair of media is the angle of incidence in the denser medium for which the angle of refraction is 90° in the rarer medium (Figure 9.22). The rays P0R0, P1R1 etc., are light rays partially reflected back into the denser medium.

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Figure 9.22

 

sin Description: 83097.png
Description: 83104.png (when the rarer medium is air)
 

When the angle of incidence is increased beyond the critical angle, light is completely reflected back into the denser medium following the laws of reflection. This phenomenon is called total internal refraction.

Some consequences of total internal reflection are as follows:
  1. The sparkle or brilliance of a cut diamond is due to total internal reflection.
  2. An empty test tube held obliquely in water and observed from above appears silvery.
  3. Mirage is an optical illusion caused by refraction and total internal reflection.

Refraction Through a Prism

A prism is an optical medium bounded by three rectangular faces and two mutually parallel triangular faces. Of the three rectangular faces, two are well polished and are called refracting faces. The third face, which is ground, is called the base of the prism (BC).

 

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Fig. 9.23 Reflection Through Prism

 

Refractive Index in Terms of the Angle of Prism and Angle of Minimum Deviation
 
The angle between the refracting faces is called the refracting angle or the angle of the prism A. It can be shown that
 
 
Description: 83115.png

where μ is the refractive index of the prism, A is the angle of the prism and D is the angle of minimum deviation. The angle of deviation δ varies as i varies and reaches a minimum value which is called the angle of minimum deviation.

Refraction Through a Lens

A lens is an optical medium bounded by two surfaces at least one of them being spherical.
 
The basic function of a lens is to converge or diverge light rays.
 

Description: Description: 88534.png


Terms Related to Lens
 
Centre of curvature (C) The centre of the sphere of which the lens surface is a part. A lens has two centres of curvature.
Radius of curvature (R) The radius of the sphere of which the lens surface is a part. A lens has two radii of curvature.
Principal axis The line passing through the centres of curvatures of the two lens surfaces.
Optic centre (O) A point in the lens, through which a light ray passes undeviated.
Principal focus (F) The point of convergence of a parallel beam of light incident on a convex lens.
Focal length (f) The distance between the optic centre and the principal focus of lens.
Power of the lens (p) The ability of a lens to converge/diverge light rays Description: 83172.png dioptre.


Image Formation in the Lenses
 

Lens

Position of the Object

Position of the Image

Nature

Size

Convex

 

 

 

 

 

At infinity

At F other side of lens

Real and inverted

Diminished

Beyond 2F

Between F and 2F other side of lens

Real and inverted

Diminished

At 2F

At 2F other side of lens

Real and inverted

Same size as object

Between F and 2F

Beyond 2F other side of lens

Real and inverted

Magnified

At F

At infinity other side of lens

Real and inverted

Magnified

Between O and F

On same side as the object

Virtual erect

Magnified

Concave

At infinity

At F on the same side as the object

Virtual image

Always diminished

 

Any other position

Always between lens and F

Virtual image

Always diminished


Lens Equation
The quantities u, v and f for a thin lens satisfy a particular relation called the lens equation:
 
 
Description: 83204.png

Here also the sign conventions for u, v and f apply similar to optical mirrors.





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