Question

A diffraction grating is placed 1.00 m from a viewing screen. Light from a hydrogen lamp goes through the grating. A hydrogen spectral line with a wavelength of 656 nm is seen 60.0 cm to one side of the center. Then, the hydrogen lamp is replaced with an unknown lamp. A spectral line is seen on the screen 36.4 cm away from the center. What is the wavelength of this spectral line

Answer 1

λ = 396.7 nm

Step-by-step explanation:

For this exercise we use the diffraction ratio of a grating

d sin θ = m λ

in general the networks works in the first order m = 1

we can use trigonometry, remembering that in diffraction experiments the angles are small

tan θ = y / L

tan θ =
`(sin \theta)/(cos \theta)` = sin θ

sin θ = y / L

we substitute

`d \ (y)/(L)` = m λ

with the initial data we look for the distance between the lines

d =
`(m \lambda \ L)/(y)`

d = 1 656 10⁻⁹ 1.00 / 0.600

d = 1.09 10⁻⁶ m

for the unknown lamp we look for the wavelength

λ = d y / L m

λ = 1.09 10⁻⁶ 0.364 / 1.00 1

λ = 3.9676 10⁻⁷ m

λ = 3.967 10⁻⁷ m

we reduce nm

λ = 396.7 nm