Optics : Diffraction gratings.

[planesinspace]

1. I am attempting a question from a textbook but the wording or perhaps the question itself is confusing me.
*Light falls at perpendicular incidence on a transmission diffraction grating. The second order diffracted light leaving the grating is examined.
The grating has 600 slits per mm, a total width of 10 cm, and is being used to examine spectral features near a wavelength of 450 nm. How close ( in nm) can the wavelength of two spectral lines be, for the two to still be seen as two, rather than blended into a single intensity peak?

Homework Equations

Ok so I have done question son diffraction gratings before, but all straightforward, and using the equation d*sin theta =m*lamda

The Attempt at a Solution

i have worked out theta to be 32.6 degrees, and (not sure if this is right) but used the equation for double-slit diffraction: y=m*lamda*D/d and worked out the spacing between the maximum and the first minimum, y, to be 0.05389m. Is this at all on the right track or am I totally lost?

I fear the latter. Any help much appreciated!

 

[alphysicist]

I think you want to look up the formulas dealing with resolving power. There is one that gives the resolving power needed to differentiate two close wavelengths in this experiment; and there is another that gives the resolving power of a specific diffraction grating that depends on the order number.

 

[planesinspace]

Thanks, i found the equation R=lamda/deltalamda
and R=mN, where N is the number of gratings and m the order.
So i basically worked out R from the second equation where I have both m and N, then I plugged it into the first and got 3.75x10^-12 m for delta lamda, is that on the right track?

 

[alphysicist]

That looks right to me.