Methods for obtaining Coherent Sources: Young’s Double Slit Fresnel’s Biprism Lloyd’s Mirror Thin Film  179º

Fresnel’s 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´ called angle of prism.  179º a b c S The prism is placed with the refracting edge in a way such that Sa is normal to the face bc of prism.

Fresnel biprism Screen O c A E Fringes of equal width S d a F B Z2 Z1

S is source A and B are coherent sources (Virtual) obtained through ‘ab’ and ‘ac’ surface of biprism Z1 = distance of biprism from source Z2 = distance of screen from biprism D= Z1+Z2 Fringes of equal width Eyepiece S A B d a b c D E F Z1 Z2 O Screen Observer measures fringe width. Ques: Can we determine Wavelength of source through this setup ? Ans: Yes d = distance between the sources A and B.

Displacement Method from magnification formula, for L1 we have In this method, the distance between the slit and the eye-piece is kept more than four times the focal length of a convex lens of short focal length used so that the two positions of the lens to form the images of S1 and S2 are found. A convex lens of short focal length is placed between the biprism and the eye-piece (as shown in fig. ). By moving the lens along the bed of the bench, two positions L1 and L2 are obtained such that the real images of S1 and S2 are obtained in the eye-piece. Let d1 and d2 be the separations between real images in the positions L1 and L2 of the lens, respectively. If ‘u’ and ‘v’ are the distances of the slit and the eye-piece from the lens in position L1 then from magnification formula, we have As the two positions of the lens are conjugate, for the second position L2 of the lens, we have Comparing eqns. (I) and (2), we get Thus, by measuring d1 and d2, d can be calculated. For accurate measurement of d, the procedure of determining d1 and d2 is repeated at least three times by moving eye-piece into different positions. from magnification formula, for L1 we have Multiplying (1) and (2) we get Similarly, for L2 Substituting the values of , d and D we can calculate the value of wavelength () of given monochromatic light.

Deviation Method δ = angle of deviation For small angles z1 δ = angle of deviation For small angles From right angle triangle and equation (1). In this method, d can be determined by using the fact that for a prism of very small refracting angle, the deviation  produced is given by Hence

If base angles are different, then Deviation Method If base angles are different, then z1 (d1+d2) α1 D µ z1 α2 In this method, d can be determined by using the fact that for a prism of very small refracting angle, the deviation  produced is given by Effect of prism angle α on fringe width??

Fringes with white light When white light is used the center fringe at O is white since all waves will constructively interfere here while the fringes on the both side of O are colored because the fringe width () depends on wavelength of light. For green light, For red light,

WHAT WILL HAPPEN? In Double slit experiment: Insert a thin transparent glass sheet of thickness t and refractive index  in the path of one beam. Fringe pattern will remain same WHAT WILL HAPPEN? or S1 S2 D d P x Any change in Fringe pattern µ t Because S1P ray will travel more path. hence effective path difference becomes

Time required for the light to reach from S1 to the point P is where ‘c’ is the velocity of light in air and ‘v’ its velocity in the medium Time required for the light to reach from S2 to the point P is The path difference (Δ) between the beams reaching P, from S1 and S2

So the path difference will be As we know So the path difference will be If P is the centre of the nth bright fringe, then At n = 0 the shift x0 is the shift for central bright fringe, so path diff is zero. Or t= x d/{D(μ-1)}=nλ/ (μ-1)}

It means that the introduction of the plate in the path of one of the interfering beams displaces the entire fringe system through a distance Note: This displacement is towards the beam in the path of which the plate is introduced. Knowing the distance through which the central fringe is shifted, D, d and  the thickness of the material ‘t’ can be calculated. We use white light to determine the thickness of the material. WHY?????? For monochromatic light central fringe will similar to other bright fringe. For white light central fringe is white.

Displacement of fringes Determine condition of net path difference. µ1,t1 C’ S1 C S2 µ2,t2 Screen Case 1: If µ1= µ2=µ and t1>t2 , Δ is positive ( upward shift) or t2>t1 , Δ is negative ( downward shift) Case 2: If t1=t2= t and 1>2 , Δ is positive ( upward shift) or 2>1 , Δ is negative ( downward shift)

Numerical In biprism experiment the eye-piece is at 120 cm away from source. The distance b/w two virtual sources was found to be equal to 0.075 cm. Find the wavelength of source, if eye-piece has to be moved through a distance 1.888 cm for 20 fringes to cross the field of view. Ans: 5900 Å The inclined faces of a glass prism of refractive index 1.5 make an angle of 1o with the base of the prism. The slit is 10 cm from the biprism and is illuminated by light of  = 5900 Å. Find the fringe width observed at a distance of 1 meter from the biprism. Ans: Fringe width= 0.338 mm (Note: Use angle α in radian)

In a biprism experiment with sodium light, bands of width 0 In a biprism experiment with sodium light, bands of width 0.1963 mm are observed at 100 cm from the slit. On introducing a convex lens 30 cm away from the slit, two images of the slit are seen 0.7 cm apart, at 100 cm distance from the slit. Calculate the wavelength of sodium light. Ans: 5889 Å 4. Interference fringes are produced in the focal plane of eye-piece 200cm away from slit. the two images are formed for each of the two positions of a convex lens placed b/w the biprism and eye-piece are found to be saperated by 4.5 mm and 2.9 mm. if the width of fringe is 0.326 mm, find the wavelength of light used. Ans: 5868 Å

Summary Superposition of two waves Double slit experiment (Division of wave front), Expression for fringe width. Displacement of fringes. Fresnel’s Biprism- Determine λ of sodium light. Fringe width Determination of ‘d’( using convex Lens). Dependence of ‘d’ on Biprism. Using white light source.