The relative index of refraction for any two of these media may be found by dividing the index (absolute) of one as given above, by the index of the other. For ordinary purposes the index of refraction gases may be considered as unity. dices given in the table above are called the “absolute ” indices. Proof. If OB is the path we must prove ᎪᏀ α = The in The triangles AGO and DEO are similar (being mutually equiangular). 1. Draw a diagram to show the path of a ray passing from air into water, and name the angles of incidence and of refraction. 2. Draw a diagram to show why a gun aimed at the apparent position of a point under water when viewed from above the surface might not be correctly aimed, and state a case when it would be. 3. Draw a diagram to show the path of a ray through a bottle having parallel sides and filled with water when the ray falls upon the side of the bottle at an oblique angle. 4. Draw a diagram to show the path of a ray passing from water into kerosene. (Kerosene is the more refractive.) 5. Determine from the following data the index of refraction for water (the index of refraction for air may be considered as unity): The angle of incidence of a ray pass ing from air into water was found to be 30° and the angle of refraction 22°. (See table, page .) 6. If a ray of light falls upon the surface of a plate of flint glass at an angle of 15°, what will be the angle of refraction within the glass? 7. On a diagram (Fig. 46) drawn to scale from the records of an experiment AB represents the surface of a liquid and COE the path of a ray incident at 0. DC measures 20 cm., and EF 12 cm. Find the index of refraction. FIG. 46. ་་་ B D FIG. 47. 8. A ray falling upon the surface of a liquid DE (Fig. 47) is deviated from its course through an angle BOC of 20°. If the angle FOA equals 40°, find the index of refraction. 9. Find the index of refraction if the angle of incidence is 40° and that of refraction is 32°. 10. Given the index of refraction (absolute) of water 1.33 and that of agate 1.54, find the index of refraction from agate to water. 11. Draw, by construction given above, the path of a ray passing from air into flint glass. (The index may be taken as .) 12. Draw, by the same construction, the path of a ray passing from a medium A to a medium B when the index between the two is . 29. Critical Angle.-It may be observed that when the incident FIG. 48. ray is in the less refractive medium there will be for every possible angle of incidence a corresponding angle of refraction. When, however, the incident ray is in the more refractive B medium there will be an angle at which the emerging ray will just lie at the separating surface as the ray AOB in the diagram. Rays incident at a greater angle will be reflected. Applying the law of sines to obtain sin COB the index of refraction, we have sin AOD α = =index. 1, and the equation becomes sine angle refraction. Whence, in general, we have, The sine of the critical angle equals the reciprocal of the index of refraction. The following geometrical method may be used for the con FIG. 49. struction of the critical angle for two media whose index of re Let SS be the separating surface, and let OA be an emerging or refracted ray from the more refractive medium below SS. find the direction of the ray incident at O it is necessary that To With O as center and a and b as radii draw circumferences. From C draw CD perpendicular to SS. Draw DOR. Then OR is the incident ray. Proof. ROE = ▲ MOD = angle of incidence; sin MOD = (a) A ray passing from water into air with refraction. (b) A ray meeting the bounding surface of water and air so as to be refracted along the surface of the water. (c) A ray totally reflected. 2. Find the critical angle of water. (See Tables for Indices of Refraction and for Sines.) 3. Find the critical angle for quartz. 4. If the critical angle for two media is 39°, what is their relative index of refraction? 5. What is the index of refraction for two media whose critical angle is 45° ? 6. Draw the construction and give proof for the critical angle for two media whose index of refraction is §. 7. For two media whose index is 1%. LV. REFRACTION BY PLATES AND PRISMS. 1. Draw a diagram to show the path of a ray of light passing obliquely through a thick plate of glass. 2. Prove by geometry that the emergent ray is parallel to the incident ray after passing through a plate with parallel sides. 3. Draw a diagram to show the real and the apparent positions of a point seen obliquely through a thick plate of glass. 4. Draw a diagram to show the path of a ray passing through a triangular prism when the angle of incidence is about 80° ? 5. Draw a diagram to show the path of a ray passing through a triangular prism when the angle of incidence is 90° ? 6. Draw a diagram to show the path of a ray passing through a triangular prism in the position of least deviation, and name the angle of deviation. 7. Draw a large prism and apply the geometrical construction of page 125 in tracing the path of a ray through the prism. 8. Show how a ray of light may be bent at right angles by a glass prism. 9. Trace the path of the ray shown incident at A in Fig. 50 through both prisms. FIG. 50. by a series of prisms. 10. Draw a diagram to show how light could be deviated through a large angle (as 120°) 11. Show by a diagram the effect produced by refraction on the direction of a ray passing through a medium of gradually increasing optical density (as through the successive layers of the atmosphere) when the incident ray strikes at an angle oblique to the planes separating the layers. 12. Show what deviation of a ray would be produced by a prism made of a less refractive material than the surrounding air, |