Question

Assume that the limits of the visible spectrum are arbitrarily chosen as 490 and 680 nm. Calculate the number of rulings per millimeter of a grating that will spread the first-order spectrum through an angle of 26.0°.

Answer 1

The number of rulings per millimeter of a grating that will spread the first-order spectrum through an angle of 26.0° is 862.07.

Step-by-step explanation:

In order to calculate the number of rulings per millimeter of a grating that will spread the first-order spectrum through an angle of 26.0°, we can use the equation:

sin(theta) = m * lambda / d

Where:

• theta is the angle of diffraction
• m is the order of the spectrum
• lambda is the wavelength of light
• d is the grating constant

By rearranging the equation, we can solve for d:

d = m * lambda / sin(theta)

In this case, we have the values:

• theta = 26.0°
• m = 1 (first-order spectrum)
• lambda = 680 nm - 490 nm = 190 nm

Converting the wavelength to millimeters:

190 nm = 0.19 μm = 0.00019 mm

Substituting the values into the equation:

d = 1 * 0.00019 mm / sin(26.0°)

Calculating, we find:

d = 0.00116 mm

Therefore, the number of rulings per millimeter of the grating is 1 / 0.00116 = 862.07.