Answer
$\lambda=5*10^{-7}m$
Work Step by Step
The angular relation of the maxima from a diffraction grating is given by
$$dsin\theta=m\lambda$$
where $d$ is the grating spacing, $m$ is the order of diffraction, $\theta$ is the angular position of the bright fringe and $\lambda$ is the wavelength of incident light.
We are given in the question, that the grating is $1cm$ wide and in that distance, there are $N=10,000$ gratings. Hence if there are $10,000$ gratings per $cm$ then the spacing between each grating is
$$d=\frac{1 cm}{10000}=10^{-6}m$$
The angle $\theta=30^{\circ}$ and $m=1$ are given to us in the question too. Hence using all this information, we can calculate the wavelength $\lambda$
$$10^{-6}sin(30)=1\lambda$$
Thus,
$$\lambda=5*10^{-7}m$$
