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Question

Light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at $$ 32.0^{\circ}, $$ what is the number of rulings per centimeter for the grating?


Solution

We use the grating equation $$ d \sin \theta=m \lambda $$ :
$$d=\dfrac{m \lambda}{\sin \theta}=\dfrac{3\left(5.00 \times 10^{-7} \mathrm{m}\right)}{\sin 32.0^{\circ}}=2.83 \times 10^{-6} \mathrm{m}$$
Thus the grating gauge is
$$\dfrac{1}{d}=3.53 \times 10^{5} \text { grooves } / \mathrm{m}=3.53 \times 10^{3} \text { grooves } / \mathrm{cm}$$

Physics
NCERT
Standard XII

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