Question

The human eye can readily detect wavelengths from about 400 nm to 700 nm.

If white light illuminates a diffraction grating having 730 lines/mm, over what range of angles does the visible m = 1 spectrum extend?

Express your answers using three significant figures separated by a comma.
θmin, θmax= ____________degrees

Answer 1

Given

that number of lines is \(\mathrm{N}=730\) lines \(/ \mathrm{mm}\)

\(=730000 \text { lines/ } \mathrm{m}\)

condition for diffraction maxima is

\(\sin \theta=m \lambda / d\)

here \(\mathrm{d}=1 / \mathrm{N}\)

for \(\lambda=400 \mathrm{nm}\)

$$ \begin{array}{l} \sin \theta=(730000)\left(400 \times 10^{-9}\right) \\ \theta_{\min }=16.97^{\sim} 17 \mathrm{deg} \end{array} $$

for wave length \(700 \mathrm{nm}\)

\(\sin \theta=(730000)\left(700 \times 10^{-9}\right)\)

\(\theta_{\max }=30.730 \text { deg }\)