Physics - Wave Optics Question with Solution | TestHub

The path difference between the waves from the two slits is given by:

$\Delta x=x_1-x_2$

$\Delta x=1.8\times 10^{-5}-1.23\times 10^{-5}=0.57\times 10^{-5}$ m $=5.7\times 10^{-6}$ m

The wavelength of the light is $\lambda =6000\times 10^{-10}$ m $=6\times 10^{-7}$ m.

Finding the ratio of path difference to wavelength:

$\frac{\Delta x}{\lambda }=\frac{5.7\times 10^{-6}}{6\times 10^{-7}}=9.5$

$\Delta x=9.5\lambda =\left(10-\frac{1}{2}\right)\lambda$

Since the path difference is an odd multiple of $\frac{\lambda }{2}$, a dark fringe is formed. The condition for the $n^{\text{th}}$ dark fringe is $\Delta x=\left(n-\frac{1}{2}\right)\lambda$.

Comparing the equations, we get $n=10$.

Thus, the $10^{\text{th}}$ dark fringe is formed.

Answer: $10^{\text{th}}$ dark