A student located on graph paper the 578 nm and 436 mm lines, and the distance between them is exactly 25 boxes (1 box = 1 mm). Another spectral line is observed to be 20 boxes from the 578 nm line and 5 boxes from the 436 nm line. What is the wavelength of this observed line? (Resolution of spectroscope= 5.68 angstroms/mm)?
The spectral line in question divides the distance between the first (578nm) and the second (436nm) at the ratio 20:5=4:1.
Therefore the unknown wavelength also divides this segment at tbe same ratio 4:1, i.e. the smaller part is 1/5 of the segment's length. The smaller part is near 436nm line.
In nanometers, the length of the segment is 578-436=142. 1/5 of this is 142/5=284/10=28.4(nm) and the unknown wavelength is
436+28.4=464.4 nm. This is the answer.