White light is passed through a double slit and interference is observed on a screen $1.5 \mathrm{~m}$ away. The separation between the slits is $0.3 \mathrm{~mm}$. The first violet and red fringes are formed $2.0 \mathrm{~mm}$ and $3.5 \mathrm{~mm}$ away from the central white fringes. The difference in wavelengths of red and voilet light is $\mathrm{nm}$.
Position of bright fringe $\mathrm{y}=\mathrm{n} \frac{\mathrm{D} \lambda}{\mathrm{d}}$
$\mathrm{y}_{1}$ of red $=\frac{\mathrm{D} \lambda_{\mathrm{r}}}{\mathrm{d}}=3.5 \mathrm{~mm}$
$\lambda_{\mathrm{r}}=3.5 \times 10^{-3} \frac{\mathrm{d}}{\mathrm{D}}$
Similarly $\lambda_{v}=2 \times 10^{-3} \frac{d}{D}$
$\lambda_{\mathrm{r}}-\lambda_{\mathrm{v}}=\left(1.5 \times 10^{-3}\right)\left(\frac{0.3 \times 10^{-3}}{1.5}\right)$
$=3 \times 10^{-7}=300 \mathrm{~nm}$
Ans. $300.0$