Question

A Michelson Interferometer using a laser source of wavelength ${\lambda }_0=500\text{nm}$ with both the mirrors $\left(M_1\text{and}{M}_2\right)$ fixed and positioned equidistant from the splitter/Combiner is shown in the figure. When a dielectric plate of refractive index $n=1.5$, of thickness $t$. is placed in front of the mirror $M_2$, a dark fringe is observed on the detector. When the dielectric plate is removed without changing the position of the mirrors $M_1$ & $M_2$, a bright fringe is observed on the detector. The minimum thickness $t$ (in nm) of the dielectric is

• A. 250

Answer 1

The correct option is A 250
From the given explanation, we can understand that, "when a tissue of thickness ${}^{\prime }{t}^{\prime }$ of refractive index ${}^{\prime }{N}^{\prime }$, is placed then a dark fringe is observed"
So,
Path difference $=\frac{{\lambda }_0}{2}$
Path difference $=2(N-1)t$
$2(N-1)t=\frac{{\lambda }_0}{2}$
$2(1.5-1)t=\frac{500\text{nm}}{2}$
$t=250\text{nm}$