What is the light's wavelength?

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In summary, a diffraction grating with 500 lines/mm is used to diffract visible light at an angle of 30°. Using the equation d*sin(θm) = mλ, it was determined that the second order (m=2) is the only possible order for the light's wavelength to fall within the visible range. This resulted in a wavelength of 500nm, as opposed to the incorrect assumption of the first order (m=1) which gave a wavelength of 1000nm.
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Homework Statement


A diffraction grating having 500 lines/mm diffracts visible light at 30°. What is the light's wavelength?

d = 1/500(lines/mm) = 2x10-6(m)
θ = 30° = pi/6 rad⇔

Homework Equations


d*sin(θm) = mλ

The Attempt at a Solution


when i rearranged the equation, i got λ = d*sin(θm)/m
And the problem was how can i find what is the order of the diffraction?
I assumed it to be the first order, so m=1, and i got the wavelength was 1000nm but the answer was 500nm, so it must be the second order, m=2. But i have no idea how to get m=2
 
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It says the grating diffracts *visible* light. The order m = 2 is the only one for which you get an answer for lambda that is in the visible range. A wavelength of 1000 nm is too large, and the wavelengths for all orders higher than 2 are too small.

That's one way I can think of to arrive at the answer. I could also be missing something else. But for now, this is what I can come up with.
 

What is the light's wavelength?

The wavelength of light refers to the distance between two consecutive peaks or troughs in a wave of light.

How is the wavelength of light measured?

The wavelength of light is typically measured in units of nanometers (nm) or meters (m). It can be measured using specialized instruments such as a spectrometer or by using mathematical equations based on the frequency of the light wave.

What factors affect the wavelength of light?

The wavelength of light can be affected by a variety of factors, including the type of material the light is traveling through, the temperature of the material, and the energy level of the light source.

What is the relationship between wavelength and frequency of light?

Wavelength and frequency of light are inversely related, meaning that as the wavelength increases, the frequency decreases and vice versa. This relationship is described by the equation: wavelength = speed of light / frequency.

Why is the wavelength of light important in science?

The wavelength of light is important in science because it can provide valuable information about the properties of light and the materials it interacts with. It is also used in various fields such as astronomy, biology, and chemistry to study the behavior of light and its interactions with matter.

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