Question

A diffraction grating 2 cm wide is able to resolve sodium d lines in second order. Find the number of rulings per mm

Answer 1

Answer:

For a diffraction grating with lines/mm = lines/inch, the slit separation is d = micrometers = x10^ m. = cm. This corresponds to an angle of θ = °

Answer 2

Answer:

The number of rulings per mm is equal to $24.554$ rulings per mm.

Explanation:

• The spectrum of sodium has two lines called D1 and D2 lines.
• When an obstacle comes in the way of a wave then the wave tends to get spread. This is called diffraction.

The formula for resolving power is given as:

$R=\frac{Y}{y} =mN$

where, $y$ is the difference in wavelength.

           $Y$ is the average wavelength.

           $m$ is the order.

           $N$ is the number of grating lines.

Step 1:

Given second-order lines so, $m=2$

Sodium d lines have wavelengths as $5890 A^{0}$ and $5896 A^{0}$.

So, average wavelength, $Y=5893 A^{0}$

The difference in wavelengths, $y=6 A^{0}$

Substituting variables in the above formula:

$\frac{5893}{6} = 2 * N$

$N=\frac{5893}{6} *(\frac{1}{2} )$

$N=491.08$ rulings.

Step 2:

Grating width $= 20$ mm

Number of rulings per mm = $(\frac{491.08}{20} )$  rulings/mm

                                            $= 24.554$ rulings per mm