Hello I really need help with this physics lab.

The lab is about the grating spectrometer.

\fConsider two slits with a separation distance d. The light passing through the slits is observed at an angle 9 with respect to the normal to the diffraction grating. As shown in gure 3.1, the ray to the left travels an extra distance D. D is calculable using trigonometry, as shown in equation 8.1. Extra distance traveled (light) D = d sin9 (3.1) Constructive interference occurs when the path difference for the two rays is exactly an integer number of wavelengths, as shown in equation 3.2. Constructive Interference D = ml = d Sin 6" (3.2) Here ' is an integer (O, 1, 2, m) ' 9,, is the corresponding angle at which constructive interference occurs ' 712. is the path difference ' Ifthe gratings have N lines per mm so d = HIM = (l/N)X10_6 m The angle for constructive interference depends on the wavelength 2., so by measuring the angle you can determine the wavelength of the light. You observe light from Mercury atoms, which is a mixture of different wavelengths (colors). You measure the angle for constructive interference from a grating for which we know the line spacing d and use equation 8.2 to calculate the wavelength 1, of the light. The telescope is initially set perpendicular to the grating (9 = 0) where all wavelengths of the beam constructively interfere, which appears as a bright white line. To observe the separated colors the spectrum, swing the telescope away from 3 = 0 until you observe separate color lines from violet to red, which comprise the n = 1 angular position for the lines of the spectrum. The angular position of the telescope for the rst appearance of a given color line to the left of the initial position is a poor estimate of 6,, for that spectrum line. To get a more accurate estimate, also measure the angular position of the telescope for the first appearance of same color line to the right of the initial position. Half of the difference between the angular positions of these two observations is a good estimate of 9,, for that color. Measuring the angular position to the left and then to the right of the perpendicular direction corrects for any error in positioning the grating perpendicular to the collimator beam. This process must be repeated for each color line in each spectrum, \"=1 and \":2, which correspond to the rst order and second order constructive interference patterns of the light. The 22:2 spectrum is more spaced out than the 72:1 spectrum. ACCEPTED VALUES In one fringe, you can typically make out four distinct color bands, similar to the spectrum shown in figure 82. 423.80" 4008\" 39.75" 44.?0\" Figure 8.2 A typical diffraction pattern for one fringe from the light emitted by Mercury A Mercury lamp emits light at specic wavelengths. The colors and wavelengths of the strongest visible lines in the Mercury spectrum are: Wavelength m Violet 404.6 moderate 407.8 weak \f