Fresnel's biprism

Aim:-To determine the wavelength of sodium light using Fresnel's biprism
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Used a biprism to get interference pattern by division of wavefront method. The biprism consist of two active angled prisms with their bases in contact. Here two sources S1 and S2 are the virtual image of the fine slit S as shown in Figure 4.3. The experimental arrangement consist of a slit S the biprism ABC and the microscope M. All are mounted on an optical bench. These are adjusted at the same height and can move and rotate as required. The light emerging from the slit fall on the biprism. The edge A of the biprism divides the incident wave front into two parts. One is through upper half AB of biprism and appears to coming from virtual source S₁. Other is from lower half AC of biprism and appears to coming virtual S₂The interference fringes are seen in the overlapping region XY and can be seen by eyepiece.

FIGURE 4.3 Fresnel’s biprism

Adjustment of Biprism: To obtain well defined interference fringes following adjustments of apparatus are required.

1. The optical bench should be levelled.
2. Slit, biprism and eyepiece should be adjusted to the same height.
3. Eyepiece should be adjusted to make fine image at crosswires.
4. The slit should be narrow and vertical.
5. Biprism is positioned in such away, may be by giving lateral movement that overlapping region should be in field of view of eyepiece.
6. The fringes so obtained should be made clear by adjusting biprism slit and eyepiece.
7. Lateral shift of the fringes should be removed with the help of biprism and eyepiece. The reason for lateral shift is that the line joining ·the slit and biprism is not parallel to the length of optical bench.
8. The bench should not be disturbed once these adjustment have been done.

Theory: On the screen at O we get a central maximum then alternatively dark, bright fringes on both sides.

(y_n)_bright =nλD                                                  … (1)

(y_n)_dark= (2n+1) λD/2d                                     …(2)

And fringe width is

Β = λD/d

(a) Determination of wavelength: Biprism can be used to determine the wavelength of given monochromatic light using the expression.

λ = βd/D

(i) Measurement of fringe width: To get β, fringes are first observed in the field of view of the microscope. The vertical wire of the eyepiece is made to coincide with one of the fringes and screw of micrometer is moved sideways and number of fringes is counted.

β =Distance moved / number of fringes passed                                  …( 5)

(ii) Measurement of D: This distance between source and eyepiece is directly measured on the optical bench scale.

(iii) Determination of D: For this we make the use of displacement method. A convex lens is placed between biprism and the eyepiece in such a way that for two positions of lens the image of virtual sources S₁ and S₂ are seen in eyepiece. Then

d = √d₁d₂                                                                           … (6)

where d1 and d2 are the distance between S₁ and S₂for two position of lens.

(b) Determination of thickness of a thin film: We know that the interference pattern shifts one side when a thin transparent film is put in the path of one ray. This shift is

δ’ = β / λ(µ- 1) t                                                           … (7)

Thus, measuring fringe width β and shift δ’ using biprism the t can be calculated if

refractive index µ and wavelength λ are known.