Question

  A source emitting light of two wavelengths is viewed through a grating spectrometer set at normal incidence. When the telescope is set at an angle of 20° to the incident direction, the second-order maximum for one wavelength is seen superposed on the third-order maximum for the other wavelength. The shorter wavelength is 400nm. Calculate the longer wavelength and the number of lines per centimeter in the grating. At what other angles, if any, can the superposition of two orders be seen using this source?

Answer 1

Given quantities:

the longer vawelength is belong to light which have a bigger nth-order maximum

$\theta = 20^o$ $m_1 = 2$ $\lambda_2= 400nm$ $m_2 = 3$ $\lambda_1 - ?$

$m_1\lambda_1= dsin\theta$ $m_1\lambda_1= m_2\lambda_2 \to \lambda_1 = \large\frac{m_2\lambda_2}{m_1}$ $= 600nm$

$m_2\lambda_2= dsin\theta$

the number of lines per centimeter in the grating $l = 1cm$

$N = \large\frac{l}{d} = \frac{lsin\theta}{m_1\lambda_1} = \frac{10^{-2}*sin20^o}{2*600*10^{-9}}$ $= 2850$