Question

In: Physics

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

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

Solutions

Expert Solution

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 \(700 \mathrm{nm}\)

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

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

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