A beam of light consists of two wavelengths, 6300 Å and 5600 Å . This beam of light is used to obtain an interference pattern in YDSE. If 4 th bright fringe of 6300 Å coincides with the n th dark fringe of 5600 Å from the central line, then find the value of n .

Step-by-step solution

Fringe width Δw 1 = 6300 Å D d and for 5600 Å ; Δw 2 = 5600 Å D d So 4 th bright fringe position of 6300 Å is at 4 × 6300 Å D d . So for n th dark fringe of 5600 Å is at n - 1 2 5600 × D d . ⇒ 4 × 6300 × D d = n - 1 2 × 5600 D d ⇒ 4 × 63 56 = n - 1 2 ⇒ n - 1 2 = 9 2 ⇒ n = 5