In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of $19.44 \mu \mathrm{~m}$ and a width of $4.05 \mu \mathrm{~m}$. The number of bright fringes between the first and the second diffraction minima is:

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Wave Optics

In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of

19.44 μ m

and a width of

4.05 μ m

. The number of bright fringes between the first and the second diffraction minima is:

Answer: (B)

The single-slit diffraction envelope sets the limits: its first minimum is at

y_{1} = \frac{D λ}{a}

and its second at

y_{2} = \frac{2 D λ}{a}

, with slit width

a = 4.05 μ

m. Inside the envelope the interference order is set by the path difference

\frac{d y}{D}

, with separation

d = 19.44 μ

m. At

y_{1}

the path difference is

\frac{d λ}{a} = \frac{19.44}{4.05} λ = 4.8 λ

, and at

y_{2}

it is

9.6 λ

. Bright fringes fall at whole-number multiples of

λ

, so between

4.8 λ

and

9.6 λ

the orders

5, 6, 7, 8, 9

appear — five bright fringes.

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option