Question

A double slit experiment is performed with light of wavelength 500nm. A thin film of thickness 2 pm and refractive index 1.5 is introduced in the path of upper beam. The location of the central maxima will:
A. Remain unstated
B. Shift downward by nearly two fringes
C. Shift upward by nearly two fringes
D. Shift downward by its fringes

Answer 1

Hint:Basically the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles. The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that later combine into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern.
In the basic version of this experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen.


Complete step by step solution:
According to the question:
Wavelength of the light $\lambda = 500nm = 500 \times {10^{ - 9}}m$
Thickness of film $t = 2\mu m = 2 \times {10^{ - 6}}m$
Refractive index of film = 1.5
Therefore extra path difference arising due to insertion of slit = $(\mu - 1)t$
$\begin{gathered}
  \therefore This \Rightarrow (\mu - 1)t = n\lambda \\
   \Rightarrow n = \dfrac{{(\mu - 1)t}}{\lambda } \\
   \Rightarrow n = \dfrac{{(1.5 - 1) \times 2 \times {{10}^{ - 6}}}}{{500 \times {{10}^{ - 9}}}} \\
   \Rightarrow n = 2 \\
\end{gathered} $
Since the thin film is inserted in the upper one, therefore, the fringe patterns will shift upwards by nearly two fringes.


Note:When a thin film is introduced in the path of one of two interfering light beams, then the entire fringe pattern is displaced towards the beam in the path of which the film is introduced.