Question

What is the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at an angle of 60.0º?

a) 1.50 μm
b) 1.75 μm
c) 2.00 μm
d) 2.25 μm

Answer 1

Using the diffraction grating equation, the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at 60.0° is approximately 0.8776 μm, which is not listed in the provided options.

Step-by-step explanation:

To find the distance between lines on a diffraction grating, we can use the diffraction grating equation,

nλ = d sin θ,

where n is the order number, λ is the wavelength of light, θ is the diffraction angle, and d is the grating spacing (the distance between adjacent lines on the grating). For a second-order maximum (n = 2), 760 nm wavelength red light, and a diffraction angle of 60.0°, we can solve for d as follows.

2(760 nm) = d sin(60.0°),

1520 nm = d (√3/2),

therefore, d = 1520 nm / (√3/2),

d = 1520 nm / 1.732,

d ≈ 877.6 nm = 0.8776 μm (or 877.6 micrometers).

This option is not listed, suggesting the provided options may not include the correct answer or there may have been a miscalculation. Always check calculations for accuracy.