The width of a single slit, if the first minimum is observed...

The width of a single slit, if the first minimum is observed at an angle of $2^{\circ}$ with a wavelength of light $6980 \AA$ is $\mathrm{mm}$
(A) $0.2$
(B) $2 \times 10^{-5}$
(C) $2 \times 10^{5}$
(D) $0.02$

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Key Concepts

Unit Conversion in Wave Optics

Accurate solutions in optics often require converting physical quantities into consistent units. For example, converting wavelengths given in Angstroms to meters or millimeters ensures that the diffraction equation is applied correctly, maintaining unit consistency throughout the calculation.

Diffraction Minimum Condition

This key concept is based on the mathematical relation a sin? = m?, where 'a' is the slit width, ? is the angle at which the m-th minimum occurs, m is the order of the minimum (usually m=1 for the first minimum), and ? is the wavelength of light. It is fundamental in analyzing and predicting the pattern produced by a single slit.

Single Slit Diffraction

This concept refers to the phenomenon that occurs when light passes through a narrow slit and spreads out, forming a pattern of bright and dark fringes on a screen. The interference between light waves emerging from different parts of the slit causes this characteristic diffraction pattern.

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