of the two verniers. The above measurements, in this method, would appear as follows: The method of averaging the entire readings of the two verniers for each setting should be avoided, as it is more cumbersome. CVII. ANGLE OF A PRISM WITH THE SPECTROMETER Measure the angle of a prism with the spectrometer by three methods. 174. Adjustment of Prism. Mounting the Prism. - Before beginning the work with the prism, the spectrometer should have been completely adjusted, as described in the preceding exercise. These adjustments must not be disturbed while placing the prism in its proper position. Mount the prism on a support with three leveling screws, place it upon the spectrometer table with one face towards the telescope, and level the prism by inspection. For convenience it is desirable that the angle between the two lines joining one of the leveling screws in the base of the prism holder to the two other screws, should be the same as the angle between the two faces of the prisms. When this is true so place the prism on its support that each of its two edges shall be perpendicular to one of these lines joining the leveling screws. Then (Fig. 89) the face AB can be leveled by the screw D without disturbing the level of the face AC; and the face AC may be leveled by the screw F without disturbing the face AB. FIG. 89. POSITION OF Before beginning the adjustment of the prism, it will be well to turn the table and telescope into all the several positions which they will later occupy in making the measurements, to observe whether it will be possible to read the two verniers of the divided circle for each of the settings. Sometimes one vernier may come under the collimator or telescope and be inaccessible. This difficulty may usually be obviated by altering the direction in which the prism stands on the table. It should also be noticed whether in these positions the prism faces are in the most advantageous relations to the objectives of the collimator and telescope. The best position is not always that in which the prism holder is centrally placed on the spectrometer table. .L C To adjust the Prism. The two prism faces must be parallel to the vertical axis of the spectrometer table (or of the telescope). Arrange the collimating eyepiece and light to observe the reflected image of the cross wires from the first face of the prism, as described in Art. 172. By turning the spectrometer table and by altering the leveling screws in the prism support only, bring the reflected cross into coincidence with the direct image. The first face is then in position. Turn the spectrometer table till the cross wires are seen reflected from the second face of the prism, and by the principle illustrated in Fig. 89 adjust the second T P T2 FIG. 90. ANGLE OF PRISM METHOD I face. This should not have disturbed the first face; but reobserve the cross in the first face, correcting any displacement which may have occurred. Continue thus until the reflected image from either face coincides with the direct image, when the prism will be in adjustment. 175. Angle of Prism; First Method. Without Collimating Eyepiece; Table fixed, Telescope movable.- Place a light, L (Fig. 90), to illuminate the slit. Turn the prism P with its refracting edge toward the collimator C, dividing the beam of light, part falling on one face of the prism and part on the other. The exact position of the prism is not important. Clamp all the movable parts of the spectrometer except the telescope. Set the telescope in the position T1, on the image of the slit reflected from the first prism face. Read the explained in Art. 173. two verniers of the divided circle, as Turn the telescope to the position T2, and set on the image of the slit reflected from the second face. The angle through which the telescope has been turned is twice the prism angle. For (Fig. 91) it has moved through the angle b+ A+ c. It is evident that the three angles b are all equal, and the same is true of the three angles c; also b+c is equal to 4; therefore b+A+c=24, twice the prism angle. T 176. Angle of Prism; Second Method. Without Collimating Eyepiece; Table movable, Telescope fixed. Turn the telescope of the spectrometer as near to the collimator as is convenient, and clamp all parts except the table. Illuminate the slit. Rotate the table until the image of the slit, reflected from one face of the prism, is set on the cross wires of the telescope (Fig. 92). Read the two verniers, as described in Art. 173. Rotate the table to bring the second prism' face into position to reflect the image of the slit to the cross wires. The angle through which the table has been turned is the supplement of the prism angle; for in the first position the normal to one face bisects the angle between the axes of the telescope •L FIG. 92. ANGLE OF PRISM METHOD II and collimator, and in the second position the normal to the other face is turned to this same direction. The angle between the normals is the same as the angle between the two faces (Fig. 93), but the table has clearly been turned through the supplement of this angle. FIG. 93. RELATION OF 177. Angle of Prism; Third Method. With Collimating Eyepiece; either Telescope or Table fixed, the other being movable. Clamp the telescope, and arrange a light, the collimating eye- ANGLES-METHODS II AND III piece, and the prism, to obtain the direct and reflected images of the cross wires (Fig. 94), as described in Art. 172. Secure coincidence between the two images by rotating the table only, which is possible if the adjustments have not been disturbed. Read the verniers; rotate the spectrometer table till coincidence between the direct and reflected images of the cross wires is secured with the second prism face, and again read the verniers. P T L FIG. 94. ANGLE OF PRISM - METHOD III From Fig. 93 it is clear that the table has been turned through an angle which is the supplement of the prism angle. If the table is fixed, the telescope may be turned from one coincidence to the other, in which case the light must also be moved; or the spectrometer may be turned on its base, the telescope being held during the motion. This will avoid moving the light, and may keep the telescope in a more convenient position. This third method for measuring the angle between two reflecting surfaces is the most precise one. CHAPTER XVI INDEX OF REFRACTION CVIII. INDEX OF REFRACTION BY MINIMUM DEVIATION Find the index of refraction of a prism for sodium light. 178. Index of Refraction. Light moves with different velocities through different media. The ratio of its velocity in vacuum, in which its velocity is greatest, to its velocity in any other medium is the absolute index of refraction of this medium. It is not practicable to compare these velocities directly. When light passes from one medium into a second, its direction of propagation in the second medium as compared with its direction in the first is a function of the angle of incidence upon the bounding surface and of the indices of refraction of the two media. If i is the angle of incidence, r the angle of refraction, and n2 the indices of refraction of the two media, then N1 In laboratory measurements the first medium is usually air; if the index of refraction of air is taken as unity, the relative index of refraction of the second medium is In the particular case of light passing through a prism in the direction of minimum deviation, the relative index of refraction of the prism is sin } (A + D) n sin 4 |