Refraction at a Plane Surface - 2008
Refraction at a plane surface
The phenomenon of deflection of light ray from the path due to a change in its speed when it travels
from one medium to another; it is called refraction.
Absolute refractive index (n) of a particular mediumIt is the ratio of speed of light in vacuum (c) to the speed of light in the given medium (v).
c
Mathematically n =
v
Relative refractive index (n) of a pair of mediaIt is the ratio of absolute refractive index of one medium to the other.
n
Mathematically relative refractive index of medium (1) wrt medium (2) is 1 n 2 = 2 ; read as
n1
refractive index of medium (2) with respect to medium (1).
TIP- In case of refraction through glass slab absolute
real depth
object distance
refractive index n =
=
apparent depth image distance
Law s of refraction1. The incident ray, the refracted ray and the normal
drawn at point of incidence all lie in the same plane
2. For a particular pair of media and for a particular wavelength the ratio of sine of angle of incidence
to the sine of angle of refraction is always a constant.
sini
= constant
sinr
• This is also called Snell’s law.
• The ratio of sine of the angle of incidence to the sine of angle of refractive is a constant and is
the relative refractive index of the pair of media.
sini n 2
i.e.
=
=1 n 2
sinr n 1
n
v
λ
c
TIP – 1. n =
2. 1 n 2 = 2
3. 1 n 2 = 1
4. 1 n 2 = 1
v
n1
v2
λ2
Probable Questions 1.State and explain laws of refraction.(2marks)
2.State and explain Snell’s law.(2marks)
3.State the principle o f reversibility.(Ans: A light ray traveled over a path obeying laws of refraction it
can be retraced in opposite direction.1mark)
TIP – Always (1 n2 )( 2 n1 ) = 1
Lateral Shift(L S)During refraction through the optical medium the perpendicular distance between the emergent ray
and the incident ray is called the lateral shift.
Expression for lateral shift (L S)• Consider a glass slab ABCD of refractive index n2 and thickness ‘t’
as shown aside
• It is surrounded by another medium of refractive index n1, let the
medium is air
• Let us assume a light ray PQ falls at Q with an angle of incidence ‘i’
• Since the glass is denser light refracts along QR instead along QC
copyright© 2008
Dept.Of Physics, MDF(I) PU Science College,Sagar
1
Refraction at a Plane Surface - 2008
•
Let the angle of refraction is ‘r’
sin i
sin r
and to the surface CD: 2 n1 =
sin r
sin i '
1
sin i
1
sin i '
But 1 n2 =
; there fore
or sini=sini’;
=
=
sin r sin r sin r
2 n1
sin i '
This proves that the ray PQ||RS
RT
• Consider the triangle RQT; sin( i − r ) =
or RT = QR sin( i − r) ------ (1)
QR
NQ
NQ
t
• Consider another triangle NQR; cos r =
----- (2)
or QR =
=
QR
cos r cos r
• Using (2) in (1) and since RT=perpendicular distance between refracted ray and the original path,
RT=LS;
t
LS =
sin( i − r) is the expression for lateral shift
cos r
Probable Questions 4.Define lateral shift. Deduce an expression for lateral shift in a glass slab.(5marks)
5.When i=0 what is LS?(1marks)
•
Applying Snell’s law to the surface AB: 1 n2 =
Normal Shift (NS)During refraction, the apparent shift in the position of the object along the normal is called normal
shift.
Expression of normal shift (NS)Consider denser medium ABCD of refractive index n1 and depth ‘t’
surrounded by another medium of refractive index n2; assuming that (1)
is denser and medium (2) is rarer like air
According to the definition normal shift N S= apparent shift in the
position along the normal; i.e NS=OI=OP-IP ---- (1)
PR
From ∆OPR; sin i =
------ (2)
OR
PR
From ∆IPR; sin r =
------ (3)
IR
sin i
IR
Now divide (3) by (2);
=
sin r OR
Let us assume P and R are very much closer; then IR ≈IP and OR≈OP
sin i
IP
There fore the above relation becomes
=
------ (4)
sin r OP
n
sin i
Apply Snell’s law to the surface AB at R; 1 n 2 = 2 =
;
n1 sin r
IP
∴ 1 n2 =
implies IP=OP.1 n2
OP
By definition normal shift N s= real depth – apparent depth =OP – IP
 n 
Implies Ns = OP - OP. 1 n2 = OP ( 1- 1 n2 )
implies N S = t 1− 2 
 n1 
1
If n1 = n and n2 =1 (air) then N S = t 1 −  is the expression for the normal shift
 n
[ Note : Normal sift in case of two or more media in contact Ns = Ns1 + N s2 + ……



1
1
1 
implies total normal shift Ns = t1 1 −  + t2 1 −  + t3 1 −  + · · · · · · · ]
 n1 
 n2 
 n3 
copyright© 2008
Dept.Of Physics, MDF(I) PU Science College,Sagar
2
Refraction at a Plane Surface - 2008
Probable Questions 6.Define normal shift and deduce an expression for normal shift.(5mark)
7.A swimmer inside water watches a pole. How does it appear to him?
1.Streched 2.Dwarf 3.Skew 4.As it is.
Critical angle(C)Suppose a light ray is traveling from denser to rarer medium then for a pair of
media and for a given wavelength the critical angle is that angle of incidence for which
the angle of refraction is 90 o.
Let n be the refractive index of the denser medium and assuming air be the rarer medium
n
sin C
the following relation can be written; 1 n2 = 2 =
= sin C
n1 sin90
n
Other wise sinC = 2
n1
1
TIP: For air as rarer medium n air=n rarer=1;
= sin C
ndenser
Total Internal ReflectionSuppose a light ray is traveling from denser to rarer medium and if angle of incidence is greater
than critical angle then the light ray reflects back to the denser medium, this phenomenon is called total
internal reflection.
Conditions to get total internal reflection1.Light ray should move from denser medium to rarer medium
2.Angle of incidence should be greater than critical angle of the denser
medium.
Probable Questions 7.Define critical angle.(1marks)
8.What is a total internal reflection? Mention two conditions to get total internal reflection.(3mark)
Mirages on land –
During hot day time ground gets the heat and will be
radiated back to the atmosphere. The air layer just above the
ground gets more heat than the air above quite above the ground.
Consider the diagram shown aside, there is an object OA
and a light ray AB is coming from its tip A as shown. When it is
coming towards ground it feels that the air layer at the bottom
having less density than the toper, thus a low refractive indices.
When the light ray reaches B the angle of incidence if
greater than the critical angle for air, thus the light ray get
reflected along BC; it is called total internal reflection.
Suppose a person watches thus moving light ray it may appear to come from point A′. Hence an
inverted image OA′ will appear at the same position O. This is called mirage.
Probable Questions 9.How does a mirage form? Explain.(4marks)
Optical FiberAn optical fiber is a micro glass rod coated with material
of lower refractive index than glass. Suppose a light ray enters
into the glass rod so that the angle of incidence is greater than the
critical angle for glass, i.e i>C as shown the light ray reflects
back the glass rod, this is called total internal reflection. Further
the reflected ray gets multiple total internal reflections and from
the other end of the glass rod light ray comes out.
copyright© 2008
Dept.Of Physics, MDF(I) PU Science College,Sagar
3
Refraction at a Plane Surface - 2008
The cladding with a material of lower refractive index is essential to get total internal reflection and
the optical fibers are made used in the following fields;
1.In the medical field – As a tool to do endoscopes, etc.,
2.In the field of communication – As a tool to transmit optical signals, like OFC technology, etc.,
3.in the field of optical image capturing and editing
Probable Questions 10.What are optical fibers? Explain.(4marks)
11.Mention the uses of optical fiber.(2marks)
12.On what principle optical fiber works?(1mark)
copyright© 2008
Dept.Of Physics, MDF(I) PU Science College,Sagar
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