Question

In a Young’s double slit experiment $15$ fringes are observed on a small portion of the screen when light of wavelength $500nm$ is used. $10$ fringes are observed on the same section of the screen when another light source of wavelength λ is used. Then the value of λ is (nm)

Answer 1

Step 1: Given

The wavelength of light 1: ${\lambda }_1=500nm$

Fringes produced due to light 1: $n_1=15$

The wavelength of light 2: ${\lambda }_2$

Fringes produced due to light 2: $n_2=10$

Step 2: Formula used

$\frac{n_1{\lambda }_{1}D}{d}=\frac{n_2{\lambda }_{2}D}{d}$

Where D is the distance from the screen to the slits, d is the separation between the slits, ${\lambda }_1$ and ${\lambda }_2$ are the wavelength of first and second light, respectively, $n_1$ and $n_2$ are the fringes produced due to first and second light, respectively.

Step 3: Determine the required wavelength

For Young's double-slit experiment,

$$\begin{gathered} \frac{n_1{\lambda }_{1}D}{d}=\frac{n_2{\lambda }_{2}D}{d} \\ {n}_1{\lambda }_1=n_2{\lambda }_2 \\ 15\times 500=10\times {\lambda }_2 \\ {\lambda }_2=750nm \end{gathered}$$

Therefore, the value of λ is $750nm$