Question

In a young’s double-slit experiment $\mathrm{d}=1\mathrm{mm}$ and $\mathrm{D}=200\mathrm{cm}$. It is found that the $9^{\mathrm{th}}$ bright fringe is at a distance of $6.5\mathrm{mm}$ from the $2^{\mathrm{nd}}$ dark fringe of the fringe pattern. What is the wavelength of light used?

• A. $\frac{2500}{7}$
• B. $\frac{5000}{7}$
• C. $5000$
• D. $433.33\mathrm{\AA }$

Answer 1

The correct option is D

$433.33\mathrm{\AA }$

Step 1: Given data

$\mathrm{D}=200\mathrm{cm}$

$\mathrm{d}=1\mathrm{mm}$

$\mathrm{Path}\mathrm{difference}=6.5\mathrm{mm}$

Step 2: To find

We have to determine the wavelength.

Step 3: Calculate wavelength $\lambda$.

$$\begin{gathered} \text{Path difference}=\frac{9\mathrm{\lambda D}}{\mathrm{d}}-\frac{\left(2\times 2-1\right)\mathrm{\lambda D}}{2\mathrm{d}} \\ 6.5\times {10}^{-3}=\frac{9\mathrm{\lambda }\times 2}{1\times {10}^{-3}}-\frac{3\mathrm{\lambda }\times 2}{2\times {10}^{-3}} \\ \mathrm{\lambda }=433.33\times {10}^{-9}\text{m} \\ \mathrm{\lambda }=433.33\mathrm{\AA } \end{gathered}$$

Hence, option(D) is correct.