1. Yellow light of wavelength 580 nm shines on a diffraction grating with 4000 lines/cm.
A.At what angles do the first-order and second-order maxima occur?
~13.4 degrees
To determine the angles at which the first-order and second-order maxima occur for the given diffraction grating, we can use the formula for diffraction:
sin(θ) = mλ / d
where:
θ is the angle at which a maximum occurs
m is the order of the maximum (1 for first-order, 2 for second-order)
λ is the wavelength of light (580 nm or 580 × 10^(-9) m)
d is the grating spacing (distance between adjacent lines on the grating)
First, we need to find the grating spacing (d) in meters. Given that there are 4000 lines/cm, we can convert it to lines/m by dividing by 100 (since there are 100 cm in a meter):
d = 1 / (4000 lines/cm / 100 cm/m)
= 1 / (40 lines/m)
= 0.025 m
Now we can substitute the values into the formula to find the angles:
For the first-order maximum (m = 1):
sin(θ) = (1 * 580 × 10^(-9) m) / 0.025 m
θ = arcsin((1 * 580 × 10^(-9) m) / 0.025 m)
Calculate θ using the inverse sine function on a calculator or using a computer program, and you will find the angle where the first-order maximum occurs.
For the second-order maximum (m = 2):
sin(θ) = (2 * 580 × 10^(-9) m) / 0.025 m
θ = arcsin((2 * 580 × 10^(-9) m) / 0.025 m)
Again, calculate θ using the inverse sine function, and you will find the angle where the second-order maximum occurs.