A beam of light is incident normally on a diffraction grating of width 2cm. It is found that at 30 degrees, the n(adsbygoogle = window.adsbygoogle || []).push({}); ^{th}order diffraction maximum for [itex]\lambda_1 = 5 \times 10^{-5}[/itex]cm is superimposed on the (n + 1)^{th}order of [itex]\lambda_2 = 4 \times 10^{-5}[/itex]cm.

1]How many lines per cm does the grating have?

2]Find out whether the first order spectrum from such a grating can be used to resolve the wavelengths [itex]\lambda_3 = 5800[/itex] Angstrom units & [itex]\lambda_4 = 5802[/itex] Angstrom units.

My work:

1]If N ruling occupy a total width W, then slit width d=W/N.

[tex]d\sin \theta = n\lambda_1 = (n+1)\lambda_2[/tex]

[tex]{2\over N}{1\over 2} = n\lambda_1 = (n+1)\lambda_2[/tex]

[itex]5000n= 4000(n+1)[/tex] (in Angstrom units).

So, I got: n = 4; which I substituted in the first equation and I got the total number of rulingsN = 0.5 x 10^{4}

So, number of rulings per cm is: N/Total width = N/2 = 0.25 x 10^{4}

Is this part correct?

2]For this part, I can find the difference between the 2 wavelengths:

[itex]\Delta \lambda = 2[/itex] Angstrom units.

How do I determine whether the grating has good resolving power or not?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Diffraction grating

**Physics Forums | Science Articles, Homework Help, Discussion**