Question

2. Give theory of interference bands and hence obtain
an expression for fringe width.​

Answer 1

Answer:

All along the straight line passing through AA' has same thickness. therefore, a bright band is obtained at A. Let ꞵ be the distance between two bright bands Consider a point C such that thickness of the film at C is t3. If t3 is of such thickness that 2μt3cos(r+ѳ) is odd multiple of λ/2 then C will look bright.

Answer 2

Explanation:

ANSWER

We already know that the path difference 

△x=nλ for bright fringes and

△x=(n+1/2)×λ for dark fringes

Now let us study the given figure.

Suppose S1A is the perpendiculr from S1 to S2P.

Suppose,

D=OB = seperation between slits and the screen,

d = seperation between th slits

and D>>d.

Under the above approximation S1P and S2P are nearly parallel and hence S1A is very nearly perpendicular to S1P, S2P

and OP. AS S1S2 is perpendicular to OB and S1A is perpendicular to $$OP$, we have 

 ∠S2S1A=∠POB=θ 

This is a small angle as D>>d.

The path difference is 

△x=PS2−PS1≈PS2−PA 

        = S2A = dsinθ≈dtanθ

        = d×Dy 

The centers of the bright fringes are obtained atdistances y from the point B, where 

△x=d×Dy = nλ 

or, y=d