Question

Consider a double slit experiment where a parallel beam of light strikes the slit plane at an angle $\theta$ as shown. The two slits are covered with transparent plastic sheets of equal thickness t but of different refractive indices 1.2 and 1.5. The central maxima is formed at the centre of the screen at C.

• A. The sheet that was used to cover the slit $S_1$ is of refractive index 1.2
• B. The sheet that was used to cover the slit $S_1$ is of refractive index 1.5
• C. The value of $\theta$ is ${\cos }^{-1}\left[\frac{t}{10d}\right]$
• D. The value of $\theta$ is ${\cos }^{-1}\left[\frac{3t}{10d}\right]$

Answer 1

Answer: (B), (D)

The correct options are
B The sheet that was used to cover the slit $S_1$ is of refractive index 1.5
D The value of $\theta$ is ${\cos }^{-1}\left[\frac{3t}{10d}\right]$

W know that for central maxima overall path difference must be zero. Since from the source of light till slit, $S_2$ has travelled higher distance, so for $\Delta x$ to be zero at C, light has to travel higher distance from slit $S_1$ for which $S_1$ should be covered with sheet having higher refractive index i.e., 1.5.

Path difference between light wave reaching $S_2$ and $S_1$ is $\Delta x=d\cos \theta$

The geometric path length from $S_1$ to C and from $S_2$ to C is same. The difference in optical path arises due to different refractive indices of two sheets
$\Delta x=(1.5-1.2)t$
$d\cos \theta =\frac{3}{10}t\Rightarrow \cos \theta =\frac{3t}{10d}\Rightarrow \theta ={\cos }^{-1}\left[\frac{3t}{10d}\right]$