Answer:
[tex]\lambda_3 = 4.72*10^{-7} m[/tex]
Explanation:
given data:
wavelength \lambda = 708nm = 708*10^{-9} m
using the following relation:
[tex]y = \frac{mL\lambda}{d}[/tex]
according to the given information
second and third dark fringe is at same location. so
[tex]y_2 = y_3[/tex]
[tex]\frac{m_2L\lambda_2}{d} = \frac{m_3L\lambda_3}{d}[/tex]
[tex]m_2\lambda_2 = m_3\lambda_3[/tex]
[tex]2*708*10^{-9} = 3*\lambda_3[/tex]
[tex]\lambda_3 = \frac{2*708*10^{-9}}{3}[/tex]
[tex]\lambda_3 = 4.72*10^{-7} m[/tex]
