Question

Where should we place a film of refractive $\mu =1.5$ and what should be its thickness so that maxima of zero order is obtained at O.

• A. Infront of $S_1,20\mu m$
• B. Infront of $S_2,20\mu m$
• C. Infront of $S_1,10\mu m$
• D. Infront of $S_2,10\mu m$

Answer 1

The correct option is A Infront of $S_1,20\mu m$

When the thin film is placed anywhere in the path of the beam, the net path difference is given by,
$\Delta x=(\mu -1)t=n\lambda$
where $\mu$ is the refractive index of the thin film, $t$is the thickness, $n$ is the number of shifted fringes and $\lambda$ is the wavelength.
$\Delta x=S_{2}P-S_{1}P=\frac{yd}{D}$
Hence we can write,
$(\mu -1)t=\frac{yd}{D}$
$⟹t=20\mu m$
Since the pattern has to be shifted upwards, the film must be placed infront of $S_{!}$