Question

Purple light of $400nm$ passes through a pair of narrow slits, forming an interference pattern on a screen.
The diagram below is not drawn to scale, but represents paths from each of the two slits to the third "dark fringe" formed as part of the interference pattern. This is the faded spot between the second and third bright fringes.
In the diagram how much longer is path $1$ than path $2$?

• A. $400nm$
• B. $1200nm$
• C. $1600nm$
• D. $1000nm$
• E. $600nm$

Answer 1

Answer: (D)

$1000nm$

Given : $\lambda =400$ $nm$

Path difference between the lights forming nth dark fringe $\Delta x=(n-\frac{1}{2})\lambda$ where $n\ge 1$

For third dark fringe, $n=3$

$⟹$ $\Delta x=(3-\frac{1}{2})\times 400=1000$ $nm$