Light of wavelength 600 nm illuminates a diffraction grating. The second-order maximum is at angle 39.1°.
How many lines per millimeter does this grating have?
To find the number of lines per millimeter (lpmm) on the diffraction grating, we can use the equation:
d * sin(θ) = m * λ
where:
- d is the spacing between the lines on the grating,
- θ is the angle of the diffraction maximum,
- m is the order of the maximum (in this case, second-order maximum),
- λ is the wavelength of light.
In this case, we are given:
- wavelength, λ = 600 nm = 600 × 10^(-9) m
- angle, θ = 39.1°
- order, m = 2
Firstly, we need to convert the angle from degrees to radians by dividing by 180π:
θ_rad = 39.1° × (π/180)
Next, we can rearrange the equation to solve for d:
d = (m * λ) / sin(θ_rad)
Substituting the values:
d = (2 * (600 × 10^(-9) m)) / sin(39.1° × (π/180))
Finally, we can convert the spacing d into lines per millimeter (lpmm) by taking the reciprocal and multiplying by 1000:
lpmm = 1 / (d * 10^3)
Calculating this value will give you the number of lines per millimeter on the diffraction grating.
To determine the number of lines per millimeter (l/mm) on a diffraction grating, we can use the formula:
d * sin(θ) = m * λ
Where:
- d is the spacing between the grating lines (in our case, we want to find this value),
- θ is the angle of diffraction (39.1° in our case),
- m is the order of the maximum (second-order, so m = 2),
- λ is the wavelength of light (600 nm = 600 × 10^(-9) m).
Rearranging the formula, we have:
d = (m * λ) / sin(θ)
Substituting the given values:
d = (2 * 600 × 10^(-9) m) / sin(39.1°)
Using a scientific calculator, we can evaluate this expression and find the value of d. After that, we can convert d from meters to millimeters and calculate the number of lines per millimeter by taking the reciprocal.
Let's do the calculations:
Firstly, convert the angle from degrees to radians:
θ_rad = 39.1° * (π / 180°)
Then calculate the value of d:
d = (2 * 600 × 10^(-9)) / sin(θ_rad)
Next, convert d from meters to millimeters:
d_mm = d * 10^3
Finally, calculate the number of lines per millimeter:
l_mm = 1 / d_mm
Thus, by following this process, you can determine the number of lines per millimeter for the given diffraction grating.
Strictly speaking, it depends upon the angle of incidence. Assume it is zero degrees (normal).
Then use the grating equation. Let d be the groove spacing.
n*(lambda) = d sin(theta)
In your case,
lamda (the wavelength) = 600*10^-9 m
n = 2
sin(theta) = 0.6307
Solve for d in meters.
Lines per mm = 1000/d(meters)