6 Light rays enter the plane surface of a glass hemisphere of radius 5 cm and refractive index 1.5. a. Using the system matrix representing the hemisphere, de- termine the exit elevation and angle of a ray that enters parallel to the optical axis and at an elevation of 1 cm. b. Enlarge the system to a distance x beyond the hemi- sphere and find the new system matrix as a function of x. c. Using the new system matrix, determine where the ray described above crosses the optical axis.

1. Roque is flying a kite along the dolomite sand of Manila Bay. If the string is 45 meters, determine the rate at which the angle of elevation is changing if the horizontal distance from him to the point directly below the kite is 13 m. Assume that he is running at a rate of 1.2 m/s; the kite is not swaying as it flies upward; and he started from rest when the kite is directly along his field of vision. A. 0.0923 rad/s B. 0.0279 rad/s C. 0.0222 rad/s D. None of these.

In order to identify an unknown material you are asked to solve for the critical angle of the material. In order to test this you set up a beam of light that strikes the unknown substance from air (n = 1.0) at an angle of 30° with respect to the normal.  It continues on in the substance at an angle of 23° with respect to the normal.  What is the critical angle for the unknown substance?     51°     55°     60°     63°

Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45.0° with respect to the normal, and you observe the angle of refraction to be 40.3°. A. What is the index of refraction of the substance?  B. What is its likely identity?

A beam of light is incident from a liquid on the surface of transparent solid. The angle of incidence is 30°and the angle of refraction is 18°.   Draw clear physics diagram of the problem – one for each part of the problem (3 total).  label relevant angles.  Find the critical angle for this solid when it is surrounded by the liquid.    What is the angle between the reflected and refracted rays when the angle of incidence is 3°less than the critical angle?

Light traveling through medium 3 (n3 = 2.4) is incident on the interface with medium 2 (n2 = 2.0) at angle θ. If light does enter into medium 2 but no light enters into medium 1 (n1 = 1.6), what can we conclude about the range of values for θ?

a