"(II) Two plane mirrors meet at a 135° angle, Fig. 32–47. If light rays strike one mirror at 32° as shown, at what angle θ do they leave the second mirror?


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(II) A diverging lens is placed next to a converging lens of focal length ƒ_C , as in Fig. 33–14. If ƒ_T represents the focal length of the combination, show that the focal length of the diverging lens, ƒ_D , is given by

1/ƒ_D = (1/ƒ_T) - (1/ƒ_C)

(II) An aquarium filled with water has flat glass sides whose index of refraction is 1.51. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. 32–52). What is the angle of this light ray when it enters (a) the glass, and then (b) the water? (c) What would be the refracted angle if the ray entered the water directly?

(II) (a) What is the minimum index of refraction for a glass or plastic prism to be used in binoculars (Fig. 32–34) so that total internal reflection occurs at 45°? (b) Will binoculars work if their prisms (assume n = 1.58) are immersed in water? (c) What minimum n is needed if the prisms are immersed in water?

An object is placed 96.0 cm from a glass lens (n = 1.52) with one concave surface of radius 22.0 cm and one convex surface of radius 18.5 cm.

(a) Where is the final image?

(b) What is the magnification?

A series of polarizers are each rotated 10° from the previous polarizer. Unpolarized light is incident on this series of polarizers. How many polarizers does the light have to go through before it is 1/6 of its original intensity?

A diverging lens with ƒ = -36.5 cm is placed 14.0 cm behind a converging lens with ƒ = 20.0cm. Where will an object at infinity be focused?