Question

A thin transparent sheet is placed in front of a Young’s double slit. The fringe-width will
A. increase
B. decrease
C. remains same
D. become non-uniform

Answer 1

Use expression for the fringe width in Young’s double slit experiment. This expression gives the relation between the fringe width, wavelength, distance between slits and distance between the slit and screen.

Formula used:
The expression for the fringe width in Young’s double slit experiment is
$\beta = \dfrac{{\lambda D}}{d}$ …… (1)
Here, $\beta$ is the fringe width, $\lambda$ is the wavelength, $d$ is the distance between the slits and $D$ is the distance between the slit and the screen.

Complete answer:
When a thin transparent sheet is placed in front of the double slit, no physical quantities affecting the fringe width are changed.Therefore, the fringe width remains the same.Hence, the options A, B and D are incorrect.

From equation (1), it can be concluded that the fringe width depends on the wavelength $\lambda$ of the light, distance $d$ between the slits and the distance $D$ between the slit and screen.

Although a thin transparent sheet is placed in front of the double slit, the distance between the slits and the distance between the slit and screen remains the same.Since the sheet is transparent, the light will pass through the sheet and hence, the wavelength of the light will also remain unchanged.As all the quantities in the equation for fringe width remains the same, the fringe width will also remain the same.

Hence, the correct option is C.

Note: The students may assume that when the thin transparent sheet is placed in front of the double slit, the thin sheet will act as a screen and hence the distance between the slit and the screen is changed (decreased) which will affect the fringe width. But the thin sheet does not act as a screen.