Question

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

• A. $1178\times {10}^{-6}\text{m}$
• B. $1178\times {10}^{-9}\text{m}$
• C. $5890\times {10}^{-7}\text{m}$
• D. $1178\times {10}^{-12}\text{m}$

Answer 1

The correct option is A $1178\times {10}^{-6}\text{m}$

Given, $D=0.5\text{m}$, $d=0.5\text{mm}$
$\lambda =5890\AA$
Distance between first and third bright fringe $=2\beta =\frac{2\lambda D}{d}$
$=2\times \frac{5890\times {10}^{-10}\times 0.5}{0.5\times {10}^{-3}}$
$=1178\times {10}^{-6}\text{m}$