Question

Interference fringes were produced using light in a double-slit experiment. When a mica sheet of uniform thickness and refractive index 1.6 (relative to air) is placed in the path of light from one of the slits, the central fringe moves through some distance. This distance is equal to the width of 30 interference bands if light of wavelength 4800A˚ is used. The thickness (in μm) of mica is
A. 90
B. 12
C. 14
D. 24

Answer 1

Hint: We will use lateral shift formula to determine the thickness of mica. Substituting the given values in the formula we can find the thickness. The refraction index and width of the bands is mentioned in the question.

Formula used:
Lateral width
\[\overline{X}=\dfrac{\beta }{\lambda }(\mu -1)t\]

Complete answer:
In a double slit experiment interference fringes were produced and a mica sheet is placed in the path of light. The refractive index of mica sheet is 1.6. This refractive index is relative to air .This length of wavelength used in this experiment is 4800 A˚. We need to find the thickness of mica.
We will use the formula of lateral shift of the fringes
\[\overline{X}=\dfrac{\beta }{\lambda }(\mu -1)t\]
where, λ is the wavelength of light, t is time
Thickness of sheet and M is the refractive index of the material.

\[\begin{align}
  & t=\dfrac{30\beta \lambda }{\beta (\mu -1)} \\
 & =\dfrac{30\times 4800\times {{10}^{-10}}}{1.6-1} \\
 & =24\times {{10}^{-6}} \\
 & =24\mu m
\end{align}\]

So, the correct answer is “Option D”.

Additional Information:
When two or more waves travel in a coincident path and along the same medium, the two waves superimpose and form a resultant wave. This phenomenon is called interference. There are two coherent sources in double slit. Through these slits the waves come out and interfere.
When a ray of light falls on a surface, the emergent light shifts to some distance which is known as lateral shift. It depends on the thickness of the material and the refractive index.

Note:
Double slit experiment describes the dual nature of light and matter. It demonstrates that light and matter can both act as particles and waves. It displays the characteristics of classical and modern theory.