Consider a ray incident on the end of a fiber-optic cable as illustrated in the figure below. In the experiment, you will explore the behavior of the fiber as a function of the angle of incidence a. When a ray strikes the end of the fiber it is bent toward the normal. By Snell's law, the angle inside the core is sin core (no/n₁) sin a. Once inside the core, the ray travels until it strikes the cladding of the fiber. The angle of incidence at the cladding i is the complementary angle of core. If i is a small angle, the ray will propagate into the cladding and be lost from the fiber. If i is large, however, the ray will be internally reflected and bounce down the fiber. By Snell's law, the critical angle for the ray to be internally reflected is sin icrit = n₂/n₁. In the experiment, you cannot directly measure angles inside the fiber but you can measure a. Using the facts that, (i) for complementary angles, sin core = cos i, (ii) the trigonometric identity cos i = √I sin² i, and (iii) the index of refraction of air is no = 1, it can be shown that sin acrit = √√²-n². This quantity is known as the numerical aperture (N.A.) of the fiber. For a cable with a core that has an index of refraction of 1.5 and a cladding with an index of refraction of 1.25, what do you expect the critical angle acrit to be (in degrees)? 40.8 Cladding → Core → ecore refracted reflected

A ray of monochromatic light is incident on the face of a prism in the shape of an equilateral triangle (that is, the apex angle of the prism is 60.0°). The incidence angle of the light ray is 75.9°. The prism is made of a transparent material with an index of refraction of 1.460 (at the light ray's wavelength). (a) Calculate the angle of refraction at the first surface (in degrees). (Round your answer to at least one decimal place.) (b) Calculate the angle of incidence at the second surface (in degrees). (Round your answer to at least one decimal place.) (c) Calculate the angle of refraction at the second surface (in degrees). (Round your answer to at least one decimal place.) (d) Calculate the angle between the incident and emerging rays (in degrees). (Round your answer to at least one decimal place.)

A light ray traveling in air strikes the surface of a slab of glass at an angle of incidence of 50 degrees. Part of the light is rejected and part is refracted. Find the angle the refracted ray makes with respect to the normal to the air/glass interface.

A light ray travelling in medium a is refracted into medium b. The angle of incidence is 50.5° and the angle or refraction is 60.8°. Both angles are measured from the normal to the interface. What is the ratio of the index of refraction of medium a to that of medium b?

A light beam traveling in the air makes an angle θi with respect to an air-plastic interface. After it enters a rectangular block of plastic, it travels at an angle of θr with respect to the normal. Write an equation for the index of refraction of the plastic in terms of the given variables. Assume that the index of refraction for air is 1.001.00, and apply this value to your equation.

A ray of light crosses the boundary between some substance with n = 1.54 and air, going from the substance into air. If the angle of incidence is 29◦ what is the angle of refraction?   Calculate to 1decimal.

Three sheets of plastic have unknown indices of refraction.Sheet 1 is placed on top of sheet 2, and a laser beam is directed unto the sheets from above so that it strikes the interface at an angle of 26.5 degrees with the normal. The refracted beam in sheet 2 makes an angle of 31.7 degrees with the normal. The experiment is repeated with sheet 3 on top of sheet 2, and with the same angle of incidence, the refracted beam makes an angle of 36.7 degrees with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3, determine the expected angle of refraction in sheet 3?. Assume the same angle of incidence.

ray of light strikes a flat block of glass at an incidence angle of ?1 = 38.6°. The glass is 2.00 cm thick and has an index of refraction that equals ng = 1.52.   a.)What is the angle of refraction, ?2, that describes the light ray after it enters the glass from above? (Enter your answer in degrees to at least 2 decimal places.)   b.) With what angle of incidence, ?3, does the ray approach the interface at the bottom of the glass? (Enter your answer in degrees to at least 2 decimal places.)     c.) With what angle of refraction, ?4, does the ray emerge from the bottom of the glass? (Enter your answer in degrees to at least 1 decimal place.)     d.) The distance d separates the twice-bent ray from the path it would have taken without the glass in the way. What is this distance (in cm)?     e.) At what speed (in m/s) does the light travel within the glass?    f.) How many nanoseconds does the light take to pass through the glass along the angled path shown here?