Question

Q. 02:- Deduce an expression for fringe width in young's double slit experiment.

please give correctly answer and explain it depth and short
​

Answer 1

Answer:

Light rays coming from slits S

1

and S

2

interfere at point P.

From figure, S

1

P=

(y−

2

d

)

2

+D

2

Or S

1

P=

y

2

+

4

d

2

−yd+D

2

Or S

1

P=D

D

2

y

2

+

4D

d

2

−

D

2

yd

+1

As D>>d and y<<D, we neglect d

2

/4D and y

2

/D

2

.

We get

Or S

1

P=D

1−

D

2

yd

Or S

1

P=D[1−

2D

2

yd

]

Or S

1

P=D−

2D

yd

Similarly we get S

2

P=D+

2D

yd

Path difference between two light rays Δx=S

2

P−S

1

P

Or Δx=(D+

2D

yd

)−(D−

2D

yd

)=

D

yd

For constructive interference, Δx=nλ

∴

D

yd

=nλ

⟹ y=

d

nλD

Fringe width β=y

n

−y

n−1

∴ β=

d

nλD

−(n−1)

d

λD

⟹ β=

d

λD