Light of wavelength λstrikes a screen containing two slits a...

Light of wavelength $\lambda$ strikes a screen containing two slits a
distance $d$ apart at an angle $\theta_{1}$ to the normal. Determine the
angle $\theta_{m}$ at which the $m^{16}$ -order maximum occurs.

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Key Concepts

Double-Slit Interference

This concept involves the formation of an interference pattern when coherent light passes through two narrow slits. The light waves emerging from the slits overlap and interfere, producing a series of bright and dark fringes on a screen. The pattern results from the superposition of waves that have traveled different paths from the slits to points on the screen.

Path Difference and Constructive Interference

For bright (constructive interference) fringes to occur, the difference in the path lengths traveled by the two interfering light waves must be an integer multiple of the wavelength. This condition, often expressed as a relation involving the sine of the angles of incidence and observation, determines the positions of the intensity maxima in the interference pattern.

Oblique Incidence

When light strikes the double-slit setup at a non?normal angle, the effective path difference between the waves from the two slits is modified by the incident angle. This adjustment is critical in accurately predicting the angles at which constructive interference, and hence the bright fringes, will occur on the screen.

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