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AS Level Physics questions on the diffraction grating

Hi everyone, I've had a go at this particular question but I'm not sure I've got part b) right and on a) I'm really unsure. I can't find a mark scheme.

11 Answer the following questions with supporting calculations.
You are given a diffraction grating with 40 lines per mm.
a The diffraction grating is mounted on an instrument that can measure angles to within ±0.1°. Can this instrument be used to determine the individual wavelengths of spectral lines of wavelengths 589.6 nm and 589.0 nm? [6]
b White light is incident normally at the grating. Estimate the angle between the extreme ends of the spectrum for the tenth-order maxima [4]

a) I found the slit spacing to be 2.5 x 10^-5 m. As this is about two orders of magnitude greater than that of the wavlength I decided that it was not suitable for spectral lines of wavelength 0.1 micrometres (the wavelength for visible light) as diffraction effects would be negligible. The waves should pass through undiffracted.

b) I had found d (the slit spacing) to be 2.5 x 10^-5 m. n = 10. I used the equation n*lambda = d*sintheta rearranged to find theta for n=10, and then I doubled it. My answer was 25.4° to 3 s.f. Have I made a mistake somewhere?

Reply 1

Stonebridge

For part A, if you want to find out if it's possible to distinguish between those two very close wavelengths, you first need to find the angle between those two wavelengths. Then see how it compares to the resolution of your instrument (±0.1 deg)

For part B they are asking you to find the angle between red and violet light for n=10
How did you do that calculation? What values of wavelength did you use for red and violet?

Reply 2

Mr Cosine

Original post by Stonebridge

Thank you for your advice Stonebridge. I understand this now; what confused me on part A was the value of the order (n= 1, 2,3, etc) but then I realised that it was moot. And part B was straightforward as well, using 380 nm and 740 nm.

Thanks again :smile:

Reply 3

Akshajistari

How do you answer part A? I found the same question and I'm confused.

I still don't get it

This thread is 6 years old now!
What don't you get?

Reply 6

Shaln

Original post by Stonebridge

This thread is 6 years old now!
What don't you get?

Part A like how are you supposed to find angle without the value of order?

Reply 7

Stonebridge

The question is just asking if it would be possible, so in order to try it out, just put n=1.
If the separation of the 2 angles for the 2 wavelengths 589.6 nm and 589.0 nm is greater than 0.1^o then it is possible to measure the wavelength of these 2 lines.