Light shines through a single slit whose width is 5.6 ×10^-4 m. A diffraction pattern is formed

step 1 In this question we have to find out the angular position of first dark fringe and the wavelengt

Light shines through a single slit whose width is 5.6 ×10^-4...

Light shines through a single slit whose width is $5.6 \times 10^{-4} \mathrm{~m}$. A diffraction pattern is formed on a flat screen located $4.0 \mathrm{~m}$ away. The distance between the middle of the central bright fringe and the first dark fringe is $3.5 \mathrm{~mm}$. What is the wave length of the light?

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Key Concepts

Small Angle Approximation

In many diffraction experiments, the angles involved are very small, so sin? can be approximated by tan?, which is equivalent to the ratio y/D, where 'y' is the fringe displacement on the screen and 'D' is the distance to the screen. This approximation simplifies the analysis and computation of the light's wavelength.

Diffraction Minima

The positions of the dark fringes (minima) in a single-slit diffraction pattern are determined by the condition a sin? = m?, where 'a' is the slit width, '?' the diffraction angle, 'm' an integer (excluding zero), and '?' the wavelength. This relation is key to calculating the wavelength of light from the measured fringe locations.

Diffraction

Diffraction is the bending and spreading of waves when they encounter obstacles or pass through narrow openings, leading to characteristic interference patterns. This phenomenon is fundamental in understanding how wave behavior changes when encountering apertures near the size of their wavelength.

Single-Slit Diffraction

Single-slit diffraction occurs when light passes through a narrow slit and generates a spreading pattern of bright and dark regions. The pattern arises from the interference between light waves emanating from different parts of the slit, and its analysis reveals information about the wavelength and the slit dimensions.

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