Question

In a double=slit experiment, two parallel slits are illuminated first by light of wavelength $400nm$ and then by light of unknown wavelength. The fourth-order dark fringe resulting from the known wavelength of light falls in the same place on the screen as the second-order bright fringe from the unknown wavelength. The value of unknown wavelength of the light is

• A. $900nm$
• B. $700nm$
• C. $300nm$
• D. none of these

Answer 1

The correct option is B $700nm$

For dark fringe, path difference $p_d=\frac{(2n-1){\lambda }_k}{2}=\frac{7\times 400}{2}=1400nm$

For bright fringe, path difference $p_b={n\lambda }_u=2\times {\lambda }_u$

$\because p_d=p_b\Rightarrow {\lambda }_u=700nm$