# Chapter 34 optical images behind the mirror how far

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Chapter 34 Optical Images behind the mirror. How far was the mirror moved? Was it moved toward or away from the object? 1. Find the focal length of the mirror; f = ss /( s + s ) 2. Find s for f = –42.86 cm and s = –35 cm 3. Find the distance the mirror must be moved f = 42.86 cm s = fs /( s f ); s = 191 cm d = 91 cm 25*·· Parallel light from a distant object strikes the large mirror in Figure 34-54 ( r = 5 m) and is reflected by the small mirror that is 2 m from the large mirror. The small mirror is actually spherical, not planar as shown. The light is focused at the vertex of the large mirror. ( a ) What is the radius of curvature of the small mirror? ( b ) Is it convex or concave? ( a ) 1. Locate the image produced by the large mirror 2. This serves as a virtual image for the small mirror at s = –0.5 m. Find f small and r small ( b ) f < 0 1/ s = (1/2.5); s = 2.5 m 1/ f small = (1/2 – 1/0.5) m –1 ; f small = –0.667 m r small = 2 f small = –1.33 m The small mirror is convex 26 ·· A woman uses a concave makeup mirror with a radius of curvature of 1.5 m. How far from the mirror should her face be for the image to be 80 cm from her face? Since the image should be upright, it must be a virtual image behind the mirror. Given: s s = 0.8 m, f = 0.75 m; find s 1/ s + 1/( s – 80 cm) = 1/(75 cm); s = 30 cm 27 · A bird above the water is viewed by a scuba diver submerged beneath the water's surface directly below the bird. Does the bird appear to the diver to be closer to or farther from the surface than it actually is? The bird appears to be farther from the surface than it actually is (see Equ. 34-7). 28 · A sheet of paper with writing on it is protected by a thick glass plate having an index of refraction of 1.5. If the plate is 2 cm thick, at what distance beneath the top of the plate does the writing appear when it is viewed from directly overhead? Use Equ. 34-7 s ′ = (2/1.5) cm = 1.33 cm below the glass surface 29* · A fish is 10 cm from the front surface of a fish bowl of radius 20 cm. ( a ) Where does the fish appear to be to someone in air viewing it from in front of the bowl? ( b ) Where does the fish appear to be when it is 30 cm from the front surface of the bowl? ( a ) 1. The object is inside the bowl; determine r 2. Use Equ. 34-5; n 1 = 1.33, n 2 = 1.0, s = 10 cm ( b ) Repeat ( a ) for s = 30 cm r = –20 cm s = –8.58 cm; 8.58 cm from the front surface of the bowl. s = –35.9 cm; 35.9 cm from the front surface of the bowl. 30 ·· A very long glass rod of 2-cm diameter has one end ground to a convex spherical surface of radius 5 cm. Its index of refraction is 1.5. ( a ) A point object in air is on the axis of the rod 20 cm from the surface. Find the image and state whether it is real or virtual. Repeat for ( b ) an object 5 cm from the surface and ( c ) an object very far from the surface. Draw a ray diagram for each case. ( a ), ( b ), ( c ) Use Equ. 34-5; n 1 = 1, n 2 = 1.5; ( a ) s = 30 cm; the image is real

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