= Solution
For normal incidence, the first-order maximum of a <diffraction grating> obeys $s\sin\theta=\lambda$. Differentiating at $\lambda_0$ gives
$$
s\cos\theta_0\,\delta\theta=\delta\lambda,\qquad \theta_0=\sin^{-1}(\lambda_0/s).
$$
Therefore the positive first-order peaks are separated by
$$
\boxed{\delta\theta\simeq\frac{\delta\lambda}{s\cos\theta_0}=\frac{\delta\lambda}{\sqrt{s^2-\lambda_0^2}}.}
$$
The larger wavelength is diffracted farther from the normal. Both first orders must exist, $\lambda_0+\delta\lambda<s$; extremely close to grazing incidence the finite difference of the two inverse sines should replace this local approximation.
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