Question

What happens to the fringe pattern if in the path of one of the slits a glass plate which absorbs $50\%$ energy is introduced?

• A. The bright fringes become brighter and dark fringes become darker
• B. No fringes are observed
• C. The fringe width decreases
• D. None of the above

Answer 1

Answer: (D)

Intensity of dark and bright fringes is given by
$I_{D a r k}=\left(\sqrt{I_{1}} - \sqrt{I_{2}}\right)^{2}$
$I_{B r i g h t}=\left(\sqrt{I_{1}} + \sqrt{I_{2}}\right)^{2}$
When there is no glass plate
$I_{1}=I_{2}=I_{0}$
$\therefore I_{D a r k}=0$ and $I_{B r i g h t}=4I_{0}$
But when glass plate is introduced in the path of one of the slits,
$I_{2}=\frac{I_{0}}{2}$
$\therefore $ $I_{D a r k}\neq 0$ increases and $I_{B r i g h t}$ decreases.
Fringe width remains same.