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Ray optics
Physics http://www.sigmaprc.in
Ray optics
Ray optics
Physics http://www.sigmaprc.in
Refraction of lightBending of light at the interface of two media is called refraction
Denser to rarer medium
As light propagates from a densermedium to a rarer medium itbends away from normal
Rarer to denser medium
As light propagates from a rarermedium to a denser medium it bendstowards the normal
Simulationhttp://www.sigmaprc.in
Ray optics
Physics http://www.sigmaprc.in
Laws of refraction
Incident ray, refracted ray and the normal to the point of incidence – liein the same plane.
1
Snell’s law : Ratio of sine of angle of incidence to sine of angle ofrefraction is constant for a particular wavelength of light and a particularpair of media.
2
1 2sin( ) sin( )n i n r
Note : As light propagates from onemedium to another, its frequency remainsconstant while it speed and wavelengthchange accordingly
Simulationhttp://www.sigmaprc.in
Ray optics
Physics http://www.sigmaprc.in
Critical angleThe angle of incidence in denser medium for which the angle ofrefraction in rarer medium is 90o is called critical angle.
( )n n
Cn n
rarer 2
denser 1
sin
Total internal reflection
When angle of incidence in denser medium is greater than critical angle, the lightray is reflected back into the denser medium.
Such a reflected ray follows laws of reflection.
Simulationhttp://www.sigmaprc.in
n C ndenser rarer
osin( ) sin(90 )
n C ndenser rarer
sin( )
Using Snell’s law
Ray optics
Physics http://www.sigmaprc.in
Absolute refractive index and relative refractive index
Absolute refractive index : ( of a medium ) is defined as the ratio of speed oflight in vacuum to its speed in that medium.
Relative refractive index : Refractive index of one medium w.r.t. the other.
cn
c
vacuum vacuum
medium medium
n cn
n c
A B BAB
B A A
Absolute refractiveindex cannot beless than 1
Relative refractiveindex may be lessor greater than orequal to 1
Refractive index of air is approximated as 1. Refractive index of vacuum = 1
Ray optics
Physics http://www.sigmaprc.in
Parallel shift or lateral shift ( S )
Parallel shift ( S ) depends on angle of incidence and refractive indices of themedia. There is no deviation in the ray of light.
When a ray of light is incident on a parallel sided glass slab, then emergent ray isfound to be shifted parallel to the incident ray. This is called parallel shift or lateralshift.
sin( )
cos( )
t i rS
r
Simulationhttp://www.sigmaprc.in
Ray optics
Physics http://www.sigmaprc.in
Refraction through prism
msin ( ) / 2
sin / 2
A+dn
A
Under condition of minimum deviation :
Ray of light is parallel to base of prism
1 2i i i 1 2r r r
General relations
2 2d i i A 1 2A r r
Simulationhttp://www.sigmaprc.in
Ray optics
Physics http://www.sigmaprc.in
Determination of refractive index of material of prism
Determination of refractive indexof material of a prism in terms ofthe angle of prism ( A ) and angleof minimum deviation ( dm )of lightray through the prism.
Considering triangle DGF
( ) ( )d i r i r 1 1 2 2
( ) ( )d i i r r 1 2 1 2
r r 1 2 = 180Considering triangle DEF
A 90 90 = 360
Considering quadrilateral ADEF
A r r1 2=
( )d i i A 1 2
Substituting in (4) equation (1)
Comparing (2) and (3) we get1
2
A = 180 3
4
5
Ray optics
Physics http://www.sigmaprc.in
From the graph of angle of deviation as afunction of angle of incidence it is observedthat angle of deviation decreases, reaches aminimum and then again increases
At minimum deviation (dm )
A r= 2
Using snell’s law
Similarly from eq (5) we get
2i i i 1 2r r r 1and
Therefore from eq (4) we get
d i A m 2
A di =
m
2
Ar =
2
( ) ( )n i n r1 2sin sin
Considering n1 = 1 and n2 = n
6
7
8
( ) /
/
A+dn
A msin 2
sin 2
Determination of refractive index of material of prism
Substituting values of r and i fromeqs 6 and 7 we get
Ray optics
Physics http://www.sigmaprc.in
Combination of prismsWhen two prisms are aligned in the same direction then the total deviation in a rayof light is the sum of individual deviations due to each prism.
When the prisms are aligned in opposite directions then the net deviation is thedifference of individual deviations.
d d d net 1 2 d d d net 1 2
Ray optics
Physics http://www.sigmaprc.in
Silvered prismsWhen one of the refracting surfaces of a prism is silvered then a ray of light incidenton the other surface of the prism is refracted at the first surface and then reflectedat the other surface ( and does not meet the condition based on the critical angle )
Ray optics
Physics http://www.sigmaprc.in
Refraction through a thin angled prismWhen the angle of prism is very small, then the angle of deviation is also small. Inthis case, using small angle approximation we get
( ) /
/
A+dn
A msin 2
sin 2
( ) /
/
A+dn
A
2
2
nA A+d
( 1)d A n
Ray optics
Physics http://www.sigmaprc.in
Use of prism to change path of a beam
Ray optics
Physics http://www.sigmaprc.in
Dispersion of light due to prism
Dispersion : Splitting of white light into its individual components .
Cause of dispersion :Refractive index of a medium depends on wavelength ( colour ) of light.
As refractive index for red is less than that for violet, their deviations are differentand they are separated as they pass through a prism.
