Monochromatic light from a helium-neon laser (λ=632.8 nm) shines at a right angle to the surface of a diffraction grating that contains 150 500 lines / m. Determine the angles at which one would observe the second-order maxima.
Well, get ready for some "light" humor! The second-order maxima have a knack for staying in line...or at least they try to. Let's shed some comedic light on this situation!
To find the angles at which you would observe the second-order maxima, we need to use the equation:
λ = (dsinθ) / m
where λ is the wavelength of light, d is the spacing between the lines on the diffraction grating, θ is the angle at which the maxima are observed, and m is the order of the maxima.
Given that the wavelength of light (λ) is 632.8 nm and the spacing between the lines on the diffraction grating (d) is 1 / (150,500 lines/m), we can set up our equation:
632.8 nm = (1 / (150,500 lines/m)) * sinθ / 2
Now, let's apply some mathematical magic to solve for θ:
sinθ = (632.8 nm * 150,500 lines/m * 2) / 1
θ = arcsin((632.8 nm * 150,500 lines/m * 2) / 1)
With a little punchline calculation, you'll be able to determine the angles at which the second-order maxima are observed. Keep in mind, much like a comedian, the answer might be a bit facetious, so double-check your math!
To determine the angles at which one would observe the second-order maxima, we can use the formula for the diffraction grating:
nλ = d * sin(θ)
where:
- n is the order of the maximum
- λ is the wavelength of light
- d is the spacing between the lines of the grating
- θ is the angle at which the maximum occurs
In this case, we are interested in the second-order maximum (n = 2), the wavelength of light is 632.8 nm (λ = 6.328 × 10^-7 m), and the grating has 150500 lines per meter (d = 1 / 150500 m^-1).
Plugging these values into the formula, we can calculate the angle at which the second-order maximum occurs:
2 * (6.328 × 10^-7 m) = (1 / 150500 m^-1) * sin(θ)
Rearranging the equation, we have:
sin(θ) = (2 * (6.328 × 10^-7 m)) / (1 / 150500 m^-1)
= (2 * (6.328 × 10^-7 m)) * (150500 m)
= (2 * (6.328 × 10^-7 m)) * (150500)
= 1.9058
Taking the inverse sine of both sides, we find:
θ = sin^(-1)(1.9058)
Using a calculator or trigonometric tables, we can determine the angle:
θ ≈ 71.53 degrees
Therefore, the angle at which one would observe the second-order maximum is approximately 71.53 degrees.