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
$I_{Dark}={\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2$
$I_{Bright}={\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2$
When there is no glass plate
$I_1=I_2=I_0$
$\therefore I_{Dark}=0$ and $I_{Bright}=4I_0$
But when glass plate is introduced in the path of one of the slits,
$I_2=\frac{I_0}{2}$
$\therefore$ $I_{Dark}\ne 0$ increases and $I_{Bright}$ decreases.
Fringe width remains same.