Q. A mixture of light, consisting of wavelength $590\ nm$ and an unknown wavelength, illuminates Young’s double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of unknown light. From this data, the wavelength of the unknown light is
A) $393.4\ nm$
B) $885.0\ nm$
C) $442.5\ nm$
D) $776.8\ nm$
Explanation
(c) $n_{1}\lambda_{1} = n_{2}\lambda_{2} \Rightarrow 3 \times 590 = 4 \times \lambda_{2} \Rightarrow \lambda_{2} = 442.5nm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.