Question

A grating has 6000 lines per cm. Find the angular separation of the two yellow lines of mercury of wavelength 577 nm and 579 nm in the second order​

Answer 1

The the angular separation = 0.19°

• A diffraction grating is a periodic optical element used in optics that divides light into many beams that go in various directions (i.e., different diffraction angles). A type of structural colouring is the coloration that is emerging. The directions or diffraction angles of these beams depend on the wavelength of the incident light, the angle at which the wave (light) strikes the diffraction grating, and the distance or spacing between consecutive diffracting elements (such as parallel slits for a transmission grating). Grating serves as a dispersive component.
• Diffraction gratings are so frequently employed in monochromators and spectrometers, but they can also be used in other settings, such as wavefront measurement and high precision optical encoders for motion control.

Here, according to the given information, we are given that,

A grating has 6000 lines per cm.

Now, $dsin\alpha =2(lambda)_{1}$, where, d = $\frac{1}{6000} cm.$

$sin\alpha _{1} =2.(5.77).10^{-5} .6000 = 0.6924$

Similarly, $sin\alpha _{2} =$$2.(5.79).10^{-5} .6000 = 0.6948$

Then, $\alpha _{1} = 43.82$ and $\alpha _{2} = 44.01$

Then, the angular separation = 44.01 - 43.82 = 0.19°.

Hence, the the angular separation = 0.19°

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