Question

The path difference between two interfering waves at a point on screen is $70.5$times the wavelength. The point is:
Dark
Bright
Not possible
Green in colour

Answer 1

- Hint: In this question we will use the Young’s Double-slit experiment i.e. when monochromatic light passing through two narrow slits illuminates a distant screen , a characteristic pattern of bright and dark fringes is observed. This interference pattern is caused by the superposition of overlapping light waves originating from the two slits.

Complete step-by-step solution -

According to the question we have to find the point of the path difference between two interfering waves at a point on screen is $70.5$ times the wavelength.
Hence if the difference between two waves is integral multiple of wavelength, which satisfies conditions for constructive interference . Whereas , if the path difference between two waves is an odd integral multiple of half wavelength , it satisfies the condition for destruction.
As the given path difference is half of the integral multiple of wavelength , so the point is dark as destructive interference occurs at that point.

Note: Young’s double-slit experiment uses two coherent sources of light placed at a small distance apart, usually , only a few orders of magnitude greater than the wavelength of light is used. Young’s double- slit experiment helped in understanding the wave theory of light .