In Young’s double slit arrangement,
Question:

In Young’s double slit arrangement, slits are separated by a gap of $0.5 \mathrm{~mm}$, and the screen is placed at a distance of $0.5 \mathrm{~m}$ from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890A  is :-

1. $1178 \times 10^{-9} \mathrm{~m}$

2. $1178 \times 10^{-6} \mathrm{~m}$

3. $1178 \times 10^{-12} \mathrm{~m}$

4. $5890 \times 10^{-7} \mathrm{~m}$

Correct Option: 2,

Solution:

$\beta=\frac{\lambda \mathrm{D}}{\mathrm{d}}=\frac{5890 \times 10^{-10} \times 0.5}{0.5 \times 10^{-3}}$

$=589 \times 10^{-6} \mathrm{~m}$

Distance between first and third bright fringe

is $2 \beta=2 \times 589 \times 10^{-6} \mathrm{~m}$

$=1178 \times 10^{-6} \mathrm{~m}$