The complete experimental arrangement for determining the wavelength of monochromatic light with the help of Fresnel’s biprism is shown in Figure.
Suppose the light rays are deviated through an angle δ by the refracting faces of Fresnel’s biprism. If the angle of each prism is α and its refractive index is μ, then the angle of deviation is:
δ = α(μ − 1)
If the distance between the slit S and the biprism is a, then, according to Fig.,
d⁄2 = a tan δ
Since δ is very small,
tan δ = δ
Therefore,
d⁄2 = aδ
Substituting the value of δ,
d⁄2 = aα(μ − 1)
or,
d = 2aα(μ − 1)
If the distance between the biprism and the eyepiece is b, then the distance between the slit S and the eyepiece is:
D = (a + b)
If the width of the interference fringes is β, then:
β = λD⁄d
Therefore,
λ = βd⁄D
Substituting the values of d and D,
λ = β[2aα(μ − 1)]⁄ (a + b)
Thus, the wavelength of monochromatic light can be determined using Fresnel’s biprism.