Question

obtain an expression for fringe width in Young's double slit experiment for interference of light​

Answer 1

Explanation:

Expression for fringe width : Considering a point P at a distance x from C. The path difference between two waves arriving at P. So fringe width Y is defined as the distance between two consecutive dark fringe or distance between two consecutive bright fringe.

Let d = distance between the slits (two sources). P = a point at a distance from the middle of the screen where a bright fringe is formed. ... Since the fringes are equally spaced the distance between two consecutive bright or consecutive dark fringes gives fringe width.

Fringe width is the distance between consecutive dark and bright fringes. It is denoted by 'β'. In case of constructive interference fringe width remains constant throughout. It is also known as linear fringe width.

Answer 2

Answer:

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Explanation:

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