Show that whenever white light is passed through a...

Name: Problem 46, Chapter 27: Principles of Physics a Calculus Based Text
Uploaded: 2020-06-09T03:01:56-08:00
Duration: 3 min 22 s
Channel: Netra Sharma
Description: Show that whenever white light is passed through a diffraction grating of any spacing size, the violet end of the spectrum in the third order on a screen always overlaps the red end of the spectrum in the second order.

Show that whenever white light is passed through a diffraction grating of any spacing size, the violet end of the spectrum in the third order on a screen always overlaps the red end of the spectrum in the second order.

Key Concepts

Diffraction Grating Equation

This equation, given by d sin? = m?, relates the grating spacing (d), the diffraction angle (?), the order of the diffraction maximum (m), and the wavelength of light (?). It is fundamental to understanding how various wavelengths are diffracted in different orders when white light passes through a grating.

Diffraction Orders

Diffraction orders refer to the different sets of angles at which light constructive interference occurs. Each order (m = 1, 2, 3, ...) produces a separate spectrum, and different wavelengths appear at different angles for each order due to the wavelength dependence in the grating equation.

Wavelength Dependence of Diffraction

Since the diffraction angle in the grating equation depends on the wavelength, light of different colors (wavelengths) will be diffracted at different angles. This wavelength dependence is essential for resolving white light into its component colors within each diffraction order.

Overlap of Diffraction Orders

The phenomenon where the diffraction spectra for different orders overlap occurs because the angular position for a given wavelength in one order can coincide with that for another wavelength in a different order. Specifically, when comparing the third order for shorter wavelengths (violet) to the second order for longer wavelengths (red), one finds that 3?_violet equals 2?_red, resulting in the overlapping of these two spectral regions on the screen.

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