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$$\dfrac{1}{d}=3.53 \times 10^{5} \text { grooves } / \mathrm{m}=3.53 \times 10^{3} \text { grooves } / \mathrm{cm}$$PhysicsNCERTStandard XII

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