CGub 29 10° Wub 61 8 cm- Fg 39 CGpox Woox 35 cm Pivot point 50 cm

Suppose a man stands in front of a mm-or as show below. His eyes are 1.65 m above the floor and the top of his head is 0.13 m higher. Find the height above the floor of the top and bottom of the smallest minor in which he can see both the top of his head and his feet. How is this distance related to the man’s height?

A water fountain is at the center of a circular pool as shown in Figure P1.59. A student walks around the pool and measures its circumference C. Next, he stands at the edge of the pool and uses a protractor to measure the angle of elevation of his sightline to the top of the water jet. How high is the fountain?

The speed of the Earth in its orbit is 29.8 km/s. If that is the magnitude of the velocity v of the ether wind in Figure P39.3, find the angle between the velocity of light c in vacuum and the resultant velocity of light if there were an ether.

Pierre de Fermat (16011665) showed that whenever light travels from one point to another, its actual path is the path that requires the smallest time interval. This statement is known as Fermats principle. The simplest example is for light propagating in a homogeneous medium. It moves in a straight line because a straight line is the shortest distance between two points. Derive Snells law of refraction from Fermats principle. Proceed as follows. In Figure P34.54, a light ray travels from point P in medium 1 to point Q in medium 2. The two points are, respectively, at perpendicular distances a and b from the interface. The displacement from P to Q has the component d parallel to the interface, and we let x represent the coordinate of the point where the ray enters the second medium. Let t = 0 be the instant the light starts from P. (a) Show that the time at which the light arrives at Q is t=r1v1+r2v2=n1a2+x2c+n2b2+(dx)2c (b) To obtain the value of x for which t has its minimum value, differentiate t with respect to x and set the derivative equal to zero. Show that the result implies n1xa2+x2=n2(dx)b2+(dx)2 (c) Show that this expression in turn gives Snells law. n1sin1=n2sin2 Figure P34.54 Problems 54 and 55.

You stand in a flat meadow and observe two cows (Fig. P1.73). Cow A is due north of you and 15.0 m from your position. Clow B is 25.0111 from your position. From your point of view, the angle between cow A and cow H is 20.0, with cow B appearing to the right of cow A. (a) How far apart are cow A and cow B? (b) Consider the view seen by cow A. According to this cow, what is the angle between you and cow B? (c) Consider the view seen by cow B. According to this cow, what is the angle between you and cow A? Hint: What does the situation look like to a hummingbird hovering above the meadow? (d) Two stars in the sky appear to be 20.0 apart. Star A is 15.0 ly from the Earth, and star B. appearing to the right of star A. is 25.0 ly from the Earth. To an inhabitant of a planet orbiting star A. what is the angle in the sky between star B and our Sun? Figure P1.73 Your view of two cows in a meadow. Cow A U due north of you. You must rotate your eyes through an angle of 20.0 to look from cow A to cow B.

(a) The print in many books averages 3.50 mm in height. How high is the image at the print on the retina when the book is held 30.0 cm from the eye? (b) Compare the size of the print to the sizes of rods and cones in the fovea and discuss the possible details observable in the letters. (The eye-brain system can perform better because of interconnections and higher order image processing.)

Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a 800 mm focal length telephoto lens?

If the apex angle in the previous problem is 20.0° and n = 1.50, what is the value of a?

In what substance in Table 1.1 is the speed of light 2.290108 m/s?