Question

obtain the expression for width of central maxima with diagram​ plz fast

Answer 1

Answer:

Let the width of the slit be through which diffraction pattern is obtained be b and λ be the wavelength of light used.

The first minima of diffraction pattern is formed at point P on one side and at A of other side.

Path difference between the light rays reaching at point P Δx=S

2

P−S

1

P

∴ Δx=

2

b

sinθ

For first minima, path difference must be equal to

2

λ

∴

2

b

sinθ=

2

λ

OR bsinθ=λ

As θ is very small, thus sinθ≈tanθ=

D

y

OR b×

D

y

=λ ⟹y=

b

λD

Width of central maxima PA=2y=

b

2λD

⟹ PA∝b1

Hence the width of central maxima formed becomes half of its initial value as the slit width is doubled.