Two slits are separated by 0.320 mm . A beam of 500 -nm light strikes the slits, producing an in

step 1 Okay, so this problem gives us that our distance between the slits is 0 .32 millimeters. That's

Two slits are separated by 0.320 mm . A beam of 500 -nm...

Two slits are separated by $0.320 \mathrm{mm} .$ A beam of 500 -nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range $-30.0^{\circ} \leq \theta \leq 30.0^{\circ}$.

Key Concepts

Angular Constraints on Interference Patterns

Angular constraints limit the range of observation of the interference pattern, meaning only those orders m that result in angles ? within the specified limits are considered. When the interference equation is applied within a given angular range, only specific integer values of m produce maxima that fall inside this interval. Counting these allowed orders gives the number of observable interference maxima.

Constructive Interference Condition

Constructive interference occurs when the path difference between the two waves is an integer multiple of the wavelength. Mathematically, this is expressed as d sin(?) = m?, where d is the slit separation, ? is the angle from the central maximum, ? is the wavelength, and m is an integer representing the order of the fringe. This equation determines the angular positions of the maxima in the interference pattern.

Double-Slit Interference

This is a phenomenon where coherent light, when passing through two narrow and closely spaced slits, produces a pattern of bright and dark fringes on a screen. The pattern results from the superposition of light waves originating from the two slits. The constructive interference leads to bright fringes while the destructive interference gives rise to dark fringes.

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