Angular separation between two wavelengths

[socoil23]

1. using differentiation,find the angular separation in arc minutes in second order for two wavelengths 589.0 and 589.6 nanometers



2. d sin($$\theta$$)=m ($$\lambda$$)



3. i try to use D=$$\delta$$$$\theta$$/$$\delta$$$$\lambda$$
by differentating d sin($$\theta$$)=m ($$\lambda$$) i got d/m sec(thetha).this equation can be further change to D=(sinA+sinB)/$$\lambda$$sinB.
i assumed D is the separation between the wavelengths.is it the correct way to approach the problem??

 

[vela]

No, the problem is asking for the angular separation Δθ.

 

[socoil23]

No, the problem is asking for the angular separation Δθ.

thanks.now i know how to solve it. is it Δlambda/Δθ= d/m cosθ? and by using small angle approximation,cos theta = 1.so Δθ= Δlambda*m/d? i forgot to put extra info:d=(1/600)mm

 

[vela]

I think you need to be a little more careful because the problem asks you to find the separation to second order, not just first order.