A diffraction grating is used to resolve 458.2 nm and 458.22 nm light, at 3rd or

Question

A diffraction grating is used to resolve 458.2 nm and 458.22 nm light, at 3rd order. What is the minimum number of lines in the grating?

If the 4th order maximum is visible for this grading for 458.2 nm and 458.22 nm light, what is the smallest line spacing possible (in m)?

What is the grating specification (in lines/cm)?

What is the minimum width of the grating (in cm)?

If the pattern is projected on a screen located 102.1 cm away, how far from the central maximum is the 3rd maximum for 458.2 nm light located (in cm)?

Thank you so much

Explanation / Answer

mean wavelength L = (L1+L2)/2

L = (458.2 + 458.22)/2

L = 458.21 nm

change of Wavelength = dL = L2-L1

dL = 458.22 -458.2

dL = 0.02 nm

Resolving power

nN = Lmean/dL

n is order

N = 458.21 *10^-9/(0.02*10^-9 * 3)

N = 7636 lines

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d sin theta = mL

d = 4 * 458.21 *10^-9/sin 90

d = 1.83 um

------------

No. of lines per cm = 1/d = 1/(1.83 *10^-4 cm)

N = 5464 lines per cm

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minimum width d = 1/N = 1/5464

d = 1.84 *10^-4 cm

----------------------------

use Y = mLR/d

Y = 0.762 cm

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