Question

In two separate double slit experiments, an interference pattern is observed on a screen. In the first experiment, violet light (λ = 708 nm) is used and a second-order bright fringe occurs at the same location as a third-order dark fringe in the second experiment. Determine the wavelength of the light used in the second experiment.

Answer 1

Answer:

$\lambda_3 = 4.72*10^{-7} m$

Explanation:

given data:

wavelength \lambda = 708nm = 708*10^{-9} m

using the following relation:

$y = \frac{mL\lambda}{d}$

according to the given information

second and third dark fringe is at same location. so

$y_2 = y_3$

$\frac{m_2L\lambda_2}{d} = \frac{m_3L\lambda_3}{d}$

$m_2\lambda_2 = m_3\lambda_3$

$2*708*10^{-9} = 3*\lambda_3$

$\lambda_3 = \frac{2*708*10^{-9}}{3}$

$\lambda_3 = 4.72*10^{-7} m$