• # question_answer The central fringe of the interference pattern produced by light of wavelength 6000 A is found to shift to the position of 4th bright fringe after a glass plate of refractive index 1.5 is introduced. The thickness of the glass plate would be-                                   A) $4.8\,\mu m$               B) $8.23\,\mu m$C) $14.98\,\mu m$                        D) $3.78\,\mu m$

$\Delta x=\frac{dy}{D}\,\,-\,\,(\mu -1)\,t=0$ $y=(\mu -1)\,\,\frac{tD}{d}$ $4\beta =(\mu -1)\frac{tD}{d}\,\,\Rightarrow \,\,4\lambda =(\mu -1)\,t$ $t=\left( \frac{4\lambda }{\mu -1} \right)\,\,=\,\,\frac{4\times 6000\times {{10}^{-10}}}{1.5-1}$ $t\,\,=\,\,4.8\,\,\times \,\,{{10}^{-6}}$ $t\,\,=\,\,4.8\,\mu m$