Range of wavelength from white light through a diffraction grating

AI Thread Summary
A narrow beam of white light is incident on a diffraction grating with 3150 lines per cm, creating a spectrum on a screen 30 cm away. The problem involves determining the range of visible wavelengths that can pass through a 1 cm square hole positioned 5 cm from the zeroth order. The relevant equation for this scenario is Nλ = d sin(θ), which relates the wavelength to the angle of diffraction. The discussion focuses on calculating the angle corresponding to the hole's position and how it affects the range of wavelengths. The key challenge is to find the specific angles that allow visible light to pass through the defined aperture.
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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\lambda = dsin\theta

The Attempt at a Solution



\frac{\Delta\lambda}{\theta\Delta} = \frac{d}{N}\sqrt{1 - sin^2\theta}
 
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