Answer to Question #164080 in Optics for Banakeng

Question

 A diffraction grating produces a second-order principal maximum at 50.6° to the normal when being illuminated normally with light of wavelength 644nm. Calculate the number of lines per millimeter of the grating and the total number of principal maxima produced.

Answer 1

Given Parameters are:-

order, n=2

Angle, $\theta=50.6^{\circ}$

Wavelength, $\lambda=644nm=644\times 10^{-6}\text{mm}$

As we know,

$n\lambda=dsin\theta$

$2\times 644\times 10^{-9}=d\times sin50.6^{\circ}$

$\Rightarrow d=\dfrac{1288\times 10^{-6}}{sin50.6^{\circ}}$

=$1666.8\times 10^{-6}=1.67\times10^{-3}mm$

So, The number of lines per mm is $\dfrac{1}{d}=\dfrac{1}{1.67\times 10^{-3}}=598.8$

Hence The number of lines per mm is $598.8\equiv599$

As there are second order principal maxima so,

Total of $5$ images is seen on screen from which 3 are principal maxima.

Total number of maxima produced$= 3$