Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The m = 5 bright fringe of the unknown wavelength overlaps the
M = 4 bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?
A) 456 nm
B) 326 nm
C) 380 nm
D) 713 nm

Question

Quizplus · Accepted Answer

The condition for bright fringes is given by the equation $ m \lambda = d \sin \theta $. For the two wavelengths to overlap, $ m_1 \lambda_1 = m_2 \lambda_2 $. Given $ m_1 = 5 $, $ \lambda_1 = \lambda $, $ m_2 = 4 $, and $ \lambda_2 = 570 $ nm, solving $ 5 \lambda = 4 \times 570 $ gives $ \lambda = 456 $ nm.

Two Sources of Light Illuminate a Double Slit Simultaneously