Three discrete spectral lines occur at angles of 10.1^∘ 13.7^∘, and 14.8^∘ in the first-order sp

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Three discrete spectral lines occur at angles of 10.1^∘...

Three discrete spectral lines occur at angles of $10.1^{\circ}$ $13.7^{\circ},$ and $14.8^{\circ}$ in the first-order spectrum of a grating spectrometer. (a) If the grating has 3660 slits/cm, what are the wavelengths of the light? (b) At what angles are these lines found in the second-order spectrum?

Key Concepts

Diffraction Grating

A diffraction grating is an optical component featuring a periodic structure that splits and diffracts light into several beams traveling in different directions. Its operation is based on interference between light waves emerging from its multiple slits or grooves, leading to a pattern that separates various wavelengths.

Grating Equation

The grating equation, given by d sin ? = m?, relates the wavelength (?) of light to the diffraction angle (?), the order of the spectrum (m), and the grating spacing (d). This equation is fundamental in analyzing how light interacts with the grating to produce distinct spectral lines.

Diffraction Orders

Diffraction orders denote the different sets of angles at which constructive interference occurs when light is diffracted by a grating. Each order (indicated by the integer m, such as m = 1 for first order and m = 2 for second order) corresponds to different interference conditions and hence different angular positions for the spectral lines.

Spectral Lines

Spectral lines are distinct wavelengths observed in a spectrum, produced as a consequence of the direct diffractive separation of light. They represent specific portions of the spectrum and provide information about the light source, particularly when light is composed of discrete wavelengths due to emission or absorption processes.

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