Fresnel BiprismAugustin-Jean Fresnel was a French physicist who contributed significantly to the establishment of the wave theory of light and optics.

He gave a simple arrangement for the production of interference pattern.

Prism A prism is a wedge-shaped transparent body which causes incident light to be separated by color. The separation by color occurs since different colors corresponding to different wavelengths.

It is a device used to refract light, reflect it or break it up (to disperse it) into its constituent spectral colours.

A

B

C

D

E

)1(

Biprism It consists of two thin acute angled prisms joined at the bases. It is constructed as a single prism of obtuse angle of 179º. The acute angle on both side is about 30´. A portion of the incident light is refracted downward and a portion upward.

179º

179º

a

b c

The prism is placed with the refracting edge parallel to the line Source S such that Sa is normal to the face bc of prism.

a

b

c

S

S

A

B

da

b

c

D

E

FZ1 Z2

CFringes of equal width

Fringes of large width

When light incident from S on the lower portion of prismIt bents upwards and appears to come from virtual sourceB. Similarly light from S incident on the upper portion of Prism bents downwards appear to come from A.

So A and B are two virtual coherent sources.

AB = d

C is the screen

Interference fringes of equal width will be occur between EF portion of the screen. Beyond EF portion fringes of large width will be produced.

Distance between source and eyepiece = D

Since C is equidistant from A and B so at C maximum fringe intensity will occur. On both sides of C alternate bright and dark fringes will appear.

According to the previous theory the fringe width

dD

So position of bright fringes from C = dDn

Position of dark fringes from C = dDn

2)12(

n = 0,1,2,3….

So the wavelength of light will be

Dd

Determination of the distance between the two sources (d)

A convex lens (L1) is placed between the prism and eyepiece (M), such that the image of the virtual sources A and B are seen in the field of view of the eyepiece.

L1

M

Suppose the distance between the images of A and B as seen by the eyepiece is d1.

So ,

mn

uv

dd

1 ……..(1)

Eyepiece is moved horizontally to determine the fringe width.

Suppose for crossing 20 bright fringes from the field of view, the Eyepiece has moved through a distance l.So the fringe width be,

20l

L2

nm

uv

dd

2 ……..(2)

Now move the lens towards eyepiece and bring it to other positon L2

So that again images of A and B are seen clearly in the the field of view

Of eyepiece. Again if the distance between the two images be d2

Multiplying (1) and (2) we get

21

2

21 1

dddddd

Substituting the values of , d, D we calculate the value of wavelength () of given monochromatic light.

Fringes with white light

When white light is used the center fringe at C is white sinceall waves will constructively interfere here while the fringeson the both side of C are colored because the fringe width () depends on wavelength of light.

The fringe pattern in fresnel’s biprism is totally different

From that of fresnel’s mirrors.

In biprism it depends on refraction

In mirror it depends on reflection

For white light the two coherent virtual sources are produced by Refraction and the distance between the two sources depends upon the refractive index which intern depends upon the wavelength.

So, for green light the distance between the two

sources is different to that with red light.

The distance of the nth bright fringe from the centre with monochromatic light

dDny

Where

112 zd )(

1)1(2 zDny

For green light,

1)1(2 zDn

yg

gg

For red light,

1)1(2 zDny

r

rr