A student performs a standard two$-$slit interference experiment and carefully sketches the observed interference pattern. The red colored pencil used by the student may not precisely match the actual color of the coherent light source.

$$ Part $($a$)$

The position of the second$-$order maximum, corresponding to two full wavelengths of path difference from the two slits, is most nearly...

$$ Part $($b$)$

The position of the third$-$order minimum of intensity, corresponding to two and one$-$half wavelengths of path difference for rays arriving from the two slits, is most nearly...

$$ Part $($c$)$

Given that the two narrow slits in the barrier are separated by $10\mathrm{.}0$m$10\mathrm{.}0$m and the distance between the barrier and the screen is $2\mathrm{.}65$m$,$ what is the wavelength, in nanometers, of the coherent light source used to create the interference pattern?

$$ Part $($d$)$

The student wishes to repeat the using different slit separations. What is the smallest slit separation, in micrometers, that produces a first$-$order maximum?

$$ Part $($e$)$

The student wishes to create a pattern that shows exactly $11$ bright fringes to either side of the principal maximum. The screen can be made as wide as necessary, but the distance to the screen remains $2\mathrm{.}65$m$,$ and the wavelength is the same as calculated previously. What slit separation, in micrometers, would achieve this result?