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I'm trying to understand the solution to a problem from a textbook. We're asked to find the proportionality constant for $$\frac{d\sigma_{\rm elastic}}{dq^2}\propto e^{bt},$$ where q is the momentum transfer in a scattering process, defined in elastic scattering as $$q=2p\sin(\theta/2).$$ So the solution says to make the following argument: $$\frac{d\sigma_{\rm elastic}}{dq^2}=\frac{d\sigma_{\rm elastic}}{d\Omega}\frac{d\Omega}{dq^2}=\lambda/2\frac{d\sigma_{\rm elastic}}{d\Omega}.$$ Which seems to imply that $$\frac{d\Omega}{dq^2}=\lambda/2.$$ I just don't understand that step. Does anyone have any ideas?

Thanks!