# Fresnel's bi-prism

An alternative method to the classic Young's slits experiment for measuring the wavelength of light is that due to Fresnel. The apparatus is shown in the following diagram (Figure 1).

Monochromatic light from a narrow slit S falls on the bi-prism, the axis of which must be in line with the slit. The refracting angles of the bi- prism are very small, usually about 0.25o. This prism forms two virtual images of the slit S1 and S2 in the plane of S, and these two virtual images act as the sources for two sets of waves which overlap and produce an interference pattern on the screen.

The fringes are much brighter than those produced by Young's slits, because of the very much greater amount of light that can pass through the prism compared with that passing through the double slit arrangement.

The formula used is the same as for Young's slits, the only problem being the measurement of the separation of the two virtual sources S1 and S2.

This can be done by placing a convex lens between the bi-prism and the screen or eyepiece and measuring the separation (s) of the images of S1 and S2 produced by the lens. If the object and image distances (u and v) are found, the value of d can be calculated from

d/s = u/v

Using a two position method removes the need to measure u and v. If s1 and s2 are the separations of the two image slits in the two positions then:

d= [s1s2]1/2

Wavelength of light = xd/D = x[s1s2]1/2/D
where x is the fringe width.

Example problem
In a Fresnel's bi-prism experiment the refracting angles of the prism were 1.5o and the refractive index of the glass was 1.5. With the single slit 5 cm from the bi-prism and using light of wavelength 580 nm, fringes were formed on a screen 1 m from the single slit.
Calculate the fringe width.

For a thin prism:    deviation (q) = (n - 1)A = (1.5 - 1)1.5p/180 (in this case)
Therefore: S1S = [5 x 0.75(p/180] cm
However, s1s2 = 2s1s = 7.5p/180 = 0.131 cm therefore the fringe width is given by:
x = lD/d = [580x 10-7 x 100]/0.131 = 0.044 cm

© Keith Gibbs 2011