A physicist is calibrating a spectrometer that uses a diffraction grating to separate light in order of increasing wavelength

$($A$,$

$$B$,$

and

$$C$).$

He observes three distinct first$-$order spectral lines at the following respective angles

$$m

$($where m denotes order$).$

$1=13\mathrm{.}0,1=14\mathrm{.}0,1=15\mathrm{.}0$

$($a$)$

If the grating has $3,700$ grooves per centimeter, what wavelength $($in nm$)$ describes each of these spectral lines?

at $1=13\mathrm{.}0$

$$A

$=$ nmat $1=14\mathrm{.}0$

$$B

$=$ nmat $1=15\mathrm{.}0$

$$C

$=$ nm

$($b$)$

At what angle $($in degrees$)$ would each of these lines be found in the second$-$order spectrum?

for $$A

$2$

$=$for $$B

$2$

$=$for $$C

$2$

$=$