Stellar Interferometer
The smallest angular separation (θ) between two distant point sources for viewing the two images of the sources as separate with a telescope, is given by
where λ is the wavelength of light and D is the diameter of the objective of the telescope. Let the telescope objective be covered with a screen which is pierced with two parallel slits. Let the slit separation (d) be almost equal to the diameter of the objective of the telescope. A suitable value for d = D/1.22 . Now let the telescope be directed towards a distant double star so that the line joining the two stars is perpendicular to the length of either slit. Interference fringes due to the double slit will be observed in the focal plane of the objective. The condition for the first disappearance of fringes is given by
where 
is the angular separation between the two stars when the first disappearance of the fringes takes place. Similarly for the values of given by the multiple of λ/2d, disappearance of the fringes can be observed. If the double slit is avoided and the observations are made directly, the multiples can be ruled out. The angular separation is half the angle θ, where θ is the minimum angle of resolution of the telescope objective.
This method employing the principle of double slit interference is used to measure the angular diameter of the disc of a star rather than the angular separation between two stars.
Michelson in 1920, successfully used this method to find the diameters of stars. The arrangement is known as Michelson’s stellar interferometer. It consists of four mirrors M1, M2, M3, and M4 arranged as shown in the figure. L is the objective of the telescope and the two slits are kept in the paths of light reflected from the mirrors M3 and M4. Let S1 and S2 be the ends of a diameter of the star. The path of the rays of light from these two points S1 and S2 are shown in figure. The mirrors M1 and M2 are parallel. Also mirrors M3 and M4 are parallel. The mirrors M1 and M2 (and M3 and M4) face each other. Interference fringes will be observed in the field of view of the telescope. The path difference between the rays of light from M1 to L and M2 to L is zero.
In the side figure, A is the point difference of the rays of light on the mirror M2 and B is the point of incidence of the rays of light on the mirror M1. The path difference between the ray travelling from S2 (one end of the diameter of the disc of the star) and reaching A and B is equal to the distance BC.
From the Δ ABC,
θ = BC/D
or, BC = Dθ
For the first disappearance of the fringes, this path difference must be equal to 1.22λ.
Or, Dθ = 1.22λ
Or, θ = 1.22λ/D (iii)
In equation (iii), θ measures the angular diameter of the star.
In one of the experiments of Michelson, using a 100 inch reflecting telescope at Mount Wilson observatory, the disappearance of the fringes was observed when the distance between the mirrors M1 and M2 was 306.5 cm. If the average wavelength of light from the star is assumed to be 5750 Å, the angular diameter of the star can be calculated from the equation
θ = 1.22λ/D
here, λ = 5750 Å × 10-8 cm
D = 306.5 cm
= 0.04718 second of an arc
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