Question

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

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

Answer 1

The correct option is A

$1178\times {10}^{-6}m$

Solution:

Step 1: Given information:

Slits are separated by a gap, $D=0.5m$

The screen is placed at a distance, $d=0.5mm$

The slits are illuminated by monochromatic light, $\lambda =5890\AA$

Step 2: Calculate the distance between the first and the third bright fringe formed when the slits are illuminated by the monochromatic light of $5890\AA$

The distance between the first and third brilliant fringes is measured, $2\beta =\frac{2\lambda D}{d}$

$=2\times 5890\times {10}^{-10}\times \frac{0.5}{(0.5\times {10}^{-3})}$

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

Hence, the correct option is (A).