Final answer:
To find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a diffraction grating, use the formula: θ = sin⁻¹((mλ)/d), where θ is the angle, m is the order of the maximum, λ is the wavelength of light, and d is the distance between the lines on the grating. The correct answer is 27.0°.
Step-by-step explanation:
To find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a diffraction grating, we can use the formula:
θ = sin⁻¹((mλ)/d)
Where θ is the angle, m is the order of the maximum (in this case, 3), λ is the wavelength of light, and d is the distance between the lines on the grating. We are given that the wavelength is 580 nm and the number of lines per centimeter is 1500.
To find d, we can divide 1 cm by the number of lines per centimeter, which gives us 0.00067 cm.
Converting this to meters gives us 0.0000067 m.
Substituting these values into the formula, we have:
θ = sin⁻¹((3 * 580 nm) / 0.0000067 m)
Calculating this gives us an answer of approximately 27.0°.
Therefore, the correct answer is 27.0° (c).