In a Young's double slit experiment, a thin sheet of refractive index $1.6$ is used to cover one slit while a thin sheet of refractive index $1.3$ is used to cover the second slit. The thickness of both sheets are same and the wavelength of light used is $600 \mathrm{nm}$. If the central point on the screen is now occupied by what had been the ${10}^{\text{th }}$ bright fringe $\left(\mathrm{m}=10\right)$, then the thickness of covering sheets is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.