Question

In biprism experiment, a source of monochromatic light is used for a certain distance between slit and eyepiece. When the distance between two virtual sources is changed from $d_A$ to $d_B$, then the fringe width is changed from $Z_A$ to $Z_B$. The ratio $Z_A$ to $Z_B$ is

• A. $\left(\dfrac{d_A}{d_B}\right)^2$
• B. $\left(\dfrac{d_A}{d_B}\right)$
• C. $\left(\dfrac{d_B}{d_A}\right)$
• D. $\sqrt{\dfrac{d_B}{d_A}}$

Hint:

Fringe width is inversely proportional to the separation of coherent sources.

Answer 1

The Correct Option is C

Step 1: Fringe width formula in biprism experiment.
\[ Z = \frac{\lambda D}{d} \] where $\lambda$ is wavelength, $D$ is distance from slit to screen, and $d$ is separation between virtual sources.

Step 2: Writing expressions for both cases.
\[ Z_A = \frac{\lambda D}{d_A}, \quad Z_B = \frac{\lambda D}{d_B} \]
Step 3: Taking ratio.
\[ \frac{Z_A}{Z_B} = \frac{d_B}{d_A} \]
Step 4: Conclusion.
The required ratio is $\dfrac{d_B}{d_A}$.