When an object is placed a distance p in front of a spherical refracting surface with radius of curvature r, the image distance is i. If the index of refraction of the surrounding material is n1, what is the index of refraction of the refracting material? State your answer in terms of the given variables.

A laser (in red) hits the surface of a pool, is refracted at the interface and hits the bottom of the pool as shown on the drawing. The index of refraction of water is 1.33. The distances shown on the drawing are the following: L = 2.2 meters, H = 1 meters and D = 2.9 meters. What is the distance x? Express your answer in meters and keep three significant digits.

The radii of curvature of both sides of a thin converging lens are equal, R. The index of refraction of the lens is n. If we place an object at a distance of 1 m from the lens on its optical axis, the formed image is real, and its height is 1/4 of the height of the object. If the image formation is done in water with the same lens and object distance, the image is real again, but its height is four times larger than that of the object. The refractive index of water and air is 4/3 and 1, respectively.a) Find the refractive index of the lens, and its radius of curvature.Then we examine the lens when one of its sides is in water, the other is in the air.b) Find the focal length of the lens if parallel rays come from water or air to the lens, respectively.

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 core = cos i, (ii) the trigonometric identity complementary angles, sin cos i = √√1 - sin² i, shown…

The diamond in the figure is immersed in water. The figure shows a beam of light from diamond incident on surface S1 at point P. The angle of incidence on the surface $1 is 0 = 30°. The index of refraction are: nwater = 1.33; ndiamond = 2.42. Answer the following questions. a) What is the critical angle at the surface S1? b) Which path is most likely taken by the light after point P? (Choose from A/B/C/D/E) Incident light Diamond water B

A flashlight beam strikes the surface of a pane of glass (n=1.56) at a 59 degree angle to the normal.  What is the angle of refraction? Express your answer using two significant figures.

A man inside a spherical diving bell watches a fish through a window in the bell, as in the figure below. If the diving bell has radius R = 1.84 m and the fish is a distance p = 1.42 m from the window, calculate the image distance and the magnification. Neglect the thickness of the window. (Use 1.333 and 1.000 for the indices of refraction of water and air, respectively.) HINT Window R (a) the image distance (in m) -0.887 By the sign conventions for refracting surfaces, the negative image distance indicates the image is formed in front of the refracting surface (on the same side as the object). m (b) the magnification 0.883 X Need Help? Read It

A layer of liquid B floats on liquid A. A ray of light begins in liquid A and undergoes total internal reflection at the interface between the liquids when the angle of incidence exceeds 37.4°. When liquid B is replaced with liquid C, total internal reflection occurs for angles of incidence greater than 53.8°. Find the ratio ng/nc of the refractive indices of liquids B and C. Number i Units

The figure depicts a simplistic optical fiber: a plastic core (n1 light ray is incident on one end of the fiber at angle 0. The rays is to undergo total internal reflection at point A, where it encounters the core-sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of e that allows total internal reflection at A? 1.56) is surrounded by a plastic sheath (n2 = 1.44). A Number Units

An object (height = 7.7 cm) and its image are on opposite sides of a converging lens. The object is located 14.0 cm from the lens. The image is located 5.6 cm from the lens. Determine the image height (in cm). Enter the numerical part of your answer to two significant figures. Hint: Remember that the sign of the image height is significant.