Light of wavelength 630 nm is incident upon a single slit with width 0.40 mm. The figure shows

step 1 In this problem, at some angle theta, there will be a diffraction pattern from the center line.

Light of wavelength 630 nm is incident upon a single slit...

Light of wavelength $630 \mathrm{~nm}$ is incident upon a single slit with width $0.40 \mathrm{~mm}$. The figure shows the pattern observed on a screen positioned $2.0 \mathrm{~m}$ from the slit. Determine the distance from the center of the central bright fringe to the second minimum on one side.

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Key Concepts

Single Slit Diffraction

This concept involves the pattern of light and dark bands created when light passes through a single narrow aperture. The wave nature of light causes it to spread out and interfere with itself, forming regions of constructive and destructive interference on a screen.

Minima Condition (Dark Fringes)

In a single slit diffraction setup, the positions where destructive interference occurs (resulting in dark fringes) are determined by the equation a sin(?) = m?, where 'a' is the slit width, '?' is the wavelength of the light, '?' is the angle at which the minimum occurs, and 'm' is a nonzero integer. This condition is used to calculate the position of the minima on the screen.

Small Angle Approximation

When the angle ? is small, approximations such as sin(?) ? tan(?) ? ? (in radians) can be applied. This simplifies the computation of fringe positions on the screen, where the distance from the central maximum to a minimum can be approximated as y = L m? / a, with 'L' being the distance from the slit to the screen.

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