When the distance between two virtual sources is changed from $\mathrm{d}_{\mathrm{A}}$ to…

When the distance between two virtual sources is changed from $\mathrm{d}_{\mathrm{A}}$ to $\mathrm{d}_{\mathrm{B}}$, then the fringe width is changed from $\mathrm{Z}_{\mathrm{A}}$ to $\mathrm{Z}_{\mathrm{B}}$. The ratio $\mathrm{Z}_{\mathrm{A}}$ to $\mathrm{Z}_{\mathrm{B}}$ is
  1. $\left(\frac{\mathrm{d}_{\mathrm{A}}}{\mathrm{d}_{\mathrm{B}}}\right)^{2}$
  2. $\left(\frac{\mathrm{d}_{\mathrm{A}}}{\mathrm{d}_{\mathrm{B}}}\right)$
  3. $\left(\frac{\mathrm{d}_{\mathrm{B}}}{\mathrm{d}_{\mathrm{A}}}\right)$
  4. $\sqrt{\frac{\mathrm{d}_{\mathrm{B}}}{\mathrm{d}_{\mathrm{A}}}}$

Solution

Fringe width is given by $z=\frac{\lambda D}{d}$ $\therefore \frac{\mathrm{z}_{\mathrm{A}}}{\mathrm{Z}_{\mathrm{B}}}=\frac{\mathrm{d}_{\mathrm{B}}}{\mathrm{d}_{\mathrm{A}}}$ /

Asked in: MHT CET 2020 (13 Oct Shift 2)

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