Question

White light is passed through a double slit and interference is observed on a screen $1.5\, m$ away. The separation between the slits is $0.3\, mm$. The first violet and red fringes are formed $2,0\, mm$ and $3.5\, mm$ away from the central white fringes. The difference in wavelengths of red and violet light is ______$nm$.

Answer 1

Position of bright fringe $y = n \frac{ D \lambda}{ d }$
$y _{1} $ of red $=\frac{ D \lambda_{ r }}{ d }=3.5\, mm$
$\lambda_{ r }=3.5 \times 10^{-3} \frac{ d }{ D }$
Similarly $\lambda_{v}=2 \times 10^{-3} \frac{ d }{ D }$
$\lambda_{ r }-\lambda_{ v }=\left(1.5 \times 10^{-3}\right)\left(\frac{0.3 \times 10^{-3}}{1.5}\right)$
$=3 \times 10^{-7}=300 \,nm$