# Application of Fresnel Biprism

```Applications of Fresnel
Biprism

Working of Fresnel Biprism is based on the
phenomenon of interference of light waves.
Biprism is a combination of two acute angled
prisms placed base to base.In practice, it is
constructed as a single prism of obtuse angle
178° and acute angle is about 1° on both
sides.
Its two important applications are:
1) Determination of wavelength(λ) of
monochromatic light.
2) Determination of thickness of thin sheet of
transparent material.
D=distance between
source of waves &
screen.
d = distance between
virtual sources which
are produced by
refraction.
 When the light from source s falls on the lower
part of biprism,it appears to come from virtual
source s2 due to refraction. Similarly when light
from the source s falls on the upper part of
biprism ,it appears to come from the virtual
source S1. Hence,S1andS2 act as two coherent
sources.
 The point o on the screen is equidistant from
source S1 & S2,hence it has maximum
intensity.On both sides of O,alternate dark &
bright fringes are produced.
Condition for maxima : Intensity at any point
on the screen is maximum if path difference
∆=nλ
;where n=0,1,2,3…….
Condition for minima : Intensity at any point
on the screen is minimum if path difference
∆=(2n+1)λ/2
;where
n=0,1,2,3……
Expression for fringe width : Fringe width is
given as:
ß=λD/d
Lateral shift and its removal
 Lateral shift :Shifting of fringes
relative to crosswire when the
eyepiece is moved along the
bench is known as lateral shift.
 Removal of lateral shift : Line
joining the slit and edge of
biprism is made parallel to the
length of optical bench .For this,
along the breadth of bench so
that on moving the eyepiece
along the bench,no lateral shift
of fringes is observed.
In order to determine the wavelength(λ) of
monochromatic light (from source S) the following
1.)The position of slit and eyepiece and distance D are
noted.
2.) Set the crosswire of eyepiece on one particular fringe
and note the reading. Move the eyepiece and count
the number of fringes shifted. Take reading again .Find
the difference between these two readings and
calculate ß.
A convex lens between
biprism and eyepiece is
introduced . The
distance between
images of S1 and S2
(d) is measured . From
figure it is clear
 d1/d=v/u=n/m
 md1=nd……….(i)
 Move the lens
towards eyepiece and
set it to position
L2.Measure the
distance between the
two images.From fig
 d2/d=v/u=m/n
 nd2=md…….(ii)
 Multiply eq (i) &(ii)
and solving we get:
 D=√(d1d2)
 Putting values of
D,ßand d we get
 λ=ßd/D
2.) Determination of thickness of
thin sheet of transparent material
 A and B are two virtual
coherent sources.
 O be equidistant from A
and B on the screen.
 D-distance between
source and screen.
 d-distance between
virtual sources
 G-transparent glass
sheet having thickness t.
 P is any point on screen
 Let c0 be the velocity of light in air and c be the
velocity of light in the sheet
 From figure:
BP/co=(AP-t)/co +t/c
 BP=(AP-t) + (co/c) t
 But co/c=μ
 BP-AP=μt-t=(μ-1)t
 If P is the point occupied by nth fringe then path
difference
 BP-AP=nλ
 (μ-1)t=nλ where n is the number of fringes in
distance x.
 To find the number of fringes in distance x, we use a
source of white light .The fringes are coloured with the
central fringe as white .The cross wire is set at the
central white fringe and reading of micrometer is noted
.Now ,the plate is introduced from one side such that a
shift in central fringe is observed .The crosswire is
moved with the help of micrometer screw and reading
is again noted. The difference between the two
readings gives the value of shift which is equal to x .
 The source of white light is now replaced by a
monochromatic source of light and fringes are seen in
the eyepiece .The number of fringes n are calculated
by moving the micrometer through the same distance x
and thickness of sheet ‘t’ is calculated.
```
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