Two slits are separated by 0.180 mm . An interference pattern is formed on a screen 80.0 cm away

step 1 All right, so the general equation for the intensity distribution is given by i equals i max tim

Two slits are separated by 0.180 mm . An interference...

Two slits are separated by $0.180 \mathrm{mm} .$ An interference pattern is formed on a screen $80.0 \mathrm{cm}$ away by 656.3 -nm light. Calculate the fraction of the maximum intensity a distance $y=0.600 \mathrm{cm}$ away from the central maximum.

Key Concepts

Small-Angle Approximation

For situations where the distance to the screen is much larger than the separation between the slits, the angle of deviation is small. In such cases, the trigonometric function sin? can be approximated by ? (or y/D), simplifying the relationship between the fringe position on the screen (y), the slit separation, and the light wavelength.

Intensity Distribution Formula

The intensity at any point on the interference pattern is described by the formula I = I? cos²((? d y)/(? D)), where I? is the maximum intensity, d is the slit separation, ? is the wavelength, and D is the distance to the screen. This formula models how the interference of the waves results in a varying intensity across the pattern.

Double-Slit Interference

This concept explains that when coherent light illuminates two closely spaced slits, it produces a pattern of alternating bright and dark fringes on a screen due to the constructive and destructive interference of light waves emanating from the slits.

Path and Phase Difference

The phase difference between the light waves from the two slits is derived from the path difference, which is the additional distance traveled by one wave relative to the other. This phase difference, calculated as (2?/?) times the path difference, determines whether interference at a given point is constructive (bright fringe) or destructive (dark fringe).

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