a$)$ Show that a $30,000-$line$-$per$-$centimeter grating will not produce a maximum for visible light.

b$)$ What is the longest wavelength for which it does produce a first$-$order maximum?

c$)$ What is the greatest number of lines per centimeter a diffraction grating can have and produce a complete second$-$order spectrum for visible light knowing that $$max $=760$nm$?$