Laser Line

How to calculate resolution of spectrometer?

could any one tell me how to calculate optical resolution of spectrometer.I have 600lines/mm grating,40um slit,25cm focal length,335 laser line and 500-600nm spectral range.

You are missing some info: the size of the gratings (number of groves), and the order at which it is working (1st order, 2nd order). By the spectral range (500-600nm) and by the grove size (1666nm), this spectrometer is working in 3rd order.
As I understand, the laser line used is 335nm and can not be seen in this setup (out of range, maybe if working at 5th order)

Approximate formula for resolution of optical instruments is:
dv=1/B
v-frequency, B-maximum path difference.

I forgot the details, but there are two sources of spectral broadening, which you can calculate separately (ether by above approximate formula, or by detailed calculations), and add at the end, or more correctly add squares: sqrt(w1^2+w2^2).

First one is the finite size of the grating. This gives broadening of:
dk = k/(mN) or dlamgda = lambda/(mN)
k-wavevector, lambda-wavelength, m-order of grating, N-number of groves.

Second one is finite size of the slit. Grating transfers wavelength into angles, while focal distance of the mirror transfer angles into length.
dlambda = dx * g / (f*cos(beta))
g-grating width (1/600mm), f-focal length, beta-working angle.

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