Answer to Question #162548 in Optics for Keleko

Question

Parallel light consisting of 2 monochromatic radiations of wavelengths 6.0 x 10^(-5) cm and 4.0 x 10^(-5) cm falls normally on a plane transmission grating ruled with 5000 lines per cm. What is the angular separation of the second-order spectra of the two wavelengths?

Answer 1

Given,

Wavelengths are $(\lambda_1)=6.0\times10^{-5} cm$

$\lambda_2=4.0\times10^{-5} cm$

Grating rule $\frac{n}{d}=5000$ lines per cm

$\Rightarrow \sin\theta= \frac{n\Delta \lambda}{d}$

$\Rightarrow \sin\theta = 5000\times \lambda_2-\lambda_1$

$=5000\times(6\times 10^{-5}-4\times 10^{-5})$

$=5000\times 2\times 10^{-5}$

$=0.5$

$\sin\theta = \frac{1}{2}=\sin 30^\circ$

Hence, $\theta = 30^\circ$

Hence, the required angular separation be $30^\circ$