Answer to Question #164079 in Optics for SAmanta Ariel

Question

          A diffraction grating has 1.2 × 10⁴ rulings or lines uniformly spaced over a width w = 25.4mm. This grating is illuminated at normal incidence by yellow light from a sodium vapour lamp of wavelength 589nm. Determine the greatest angle at which an order can occur on either side of the center of the diffraction pattern?

Answer 1

The grafting spacing d is,

$d= \dfrac{w}{N}$ $= \dfrac{25.4\times 10^{-3}}{1.2\times10^4}=21.167 \times 10^{-7}m = 2117nm$

For diffraction pattern on either side of center n $\geq$ 1

For $\lambda$ = 589nm We have,

$dsin\theta$ = n$\lambda$

$\rightarrow \theta = sin^{-1}(\dfrac{n\lambda}{d})$

$\rightarrow sin^{-1}(\dfrac{1\times589\times10^{-9}}{2117\times10^{-9}})$

$\rightarrow sin^{-1}(0.278)$ = 16.14$\degree$

∴Ang $\geq$ θ≈16.14$\degree$