Answer;
7.238°
Explanation
From question we know that the grating has 1,970 grooves per centimeter, we can convert to from (cm) to (nm) for unit consistency
The slit separation is expressed below
d=1cm/1970
d=0.0005076
=5076nm
Then the angle (in degrees) that the red light of wavelength 640 nm appear in first order can be calculated using expression below
Sin(x)= mλ/d
Where λ= wavelength=640 nm
d=slit separation
Sin(x)= mλ/d
Sin(x)=(1×640)/5076
=0.126
sin-1(0.126)
X= 7.238°
Therefore,the angle (in degrees) that the red light of wavelength 640 nm appear in first order is 7.238°
