Physics - Wave Optics Question with Solution | TestHub

The path difference for the $n^{\text{th}}$ bright band is given by $n\lambda$.

The path difference for the $4^{\text{th}}$ bright band is $4\lambda$ and for the $5^{\text{th}}$ bright band is $5\lambda$.

The dark band formed between the $4^{\text{th}}$ and $5^{\text{th}}$ bright bands is the $5^{\text{th}}$ dark band, which corresponds to a path difference of $\left(4+\frac{1}{2}\right)\lambda =4.5\lambda$.

Given the wavelength $\lambda =6000\text{ A˚}=6000\times 10^{-8}\text{ cm}=6\times 10^{-5}\text{ cm}$.

The path difference $\Delta x=4.5\times 6\times 10^{-5}\text{ cm}=27\times 10^{-5}\text{ cm}=2.7\times 10^{-4}\text{ cm}$.

Comparing this with $x\times 10^{-4}\text{ cm}$, we get $x=2.7$.

Answer: $2.7$