Range of wavelength from white light through a diffraction grating

In summary, the range of wavelength in white light is approximately 400-700 nanometers (nm). A diffraction grating is a device that creates a spectrum of colors by diffracting light through evenly spaced parallel slits or grooves. This separation of colors is caused by the different angles at which each wavelength is diffracted. In scientific research, diffraction gratings are used to analyze light sources, study the properties of materials, and measure the wavelengths of light emitted or absorbed by substances.
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Homework Statement



A narrow beam of collimated white light falls at normal incidence upon a transmission grating with 3150 lines per cm. A spectrum is formed by the grating on a screen 30 cm away. If a 1 cm square hole is cut in the screen its inner edge being 5 cm from the zeroth order, what range of visible wavelengths passes through the hole?

Homework Equations



N[tex]\lambda[/tex] = dsin[tex]\theta[/tex]

The Attempt at a Solution



[tex]\frac{\Delta\lambda}{\theta\Delta}[/tex] = [tex]\frac{d}{N}[/tex][tex]\sqrt{1 - sin^2\theta}[/tex]
 
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What is the range of angle determined by the square hole ?

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1. What is the range of wavelength in white light?

The range of wavelength in white light is approximately 400-700 nanometers (nm). This includes all the visible colors of the rainbow, from violet to red.

2. What is a diffraction grating?

A diffraction grating is a device that consists of a large number of evenly spaced parallel slits or grooves. When light passes through the grating, it is diffracted into different directions, creating a spectrum of colors.

3. How does a diffraction grating separate white light into its component colors?

When white light enters a diffraction grating, each wavelength of light is diffracted at a slightly different angle. This causes the colors to separate, with shorter wavelengths (such as blue and violet) being diffracted at larger angles and longer wavelengths (such as red and orange) being diffracted at smaller angles.

4. What is the relationship between wavelength and color in a diffraction grating?

The relationship between wavelength and color in a diffraction grating is that shorter wavelengths (blue and violet) are diffracted at larger angles and longer wavelengths (red and orange) are diffracted at smaller angles. This is known as the dispersion of light.

5. How is a diffraction grating used in scientific research?

A diffraction grating is used in scientific research to analyze the composition of light sources and to study the properties of various materials. It is also used in spectroscopy to measure the wavelengths of light emitted or absorbed by a substance, which can provide valuable information about its chemical composition.

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