(II) Two rays A and B travel down a cylindrical optical fiber of diameter d = 75.0 μ m, length ℓ = 1.0km, and index of refraction n 1 = 1.465. Ray A travels a straight path down the fiber’s axis, whereas ray B propagates down the fiber by repeated reflections at the critical angle each time it impinges on the fiber’s boundary. Determine the extra time Δ t it takes for ray B to travel down the entire fiber in comparison with ray A (Fig. 32–58), assuming ( a ) the fiber is surrounded by air, ( b ) the fiber is surrounded by a cylindrical glass “cladding” with index of refraction n 2 = 1.460.
(II) Two rays A and B travel down a cylindrical optical fiber of diameter d = 75.0 μ m, length ℓ = 1.0km, and index of refraction n 1 = 1.465. Ray A travels a straight path down the fiber’s axis, whereas ray B propagates down the fiber by repeated reflections at the critical angle each time it impinges on the fiber’s boundary. Determine the extra time Δ t it takes for ray B to travel down the entire fiber in comparison with ray A (Fig. 32–58), assuming ( a ) the fiber is surrounded by air, ( b ) the fiber is surrounded by a cylindrical glass “cladding” with index of refraction n 2 = 1.460.
(II) Two rays A and B travel down a cylindrical optical fiber of diameter d = 75.0 μm, length ℓ = 1.0km, and index of refraction n1 = 1.465. Ray A travels a straight path down the fiber’s axis, whereas ray B propagates down the fiber by repeated reflections at the critical angle each time it impinges on the fiber’s boundary. Determine the extra time Δt it takes for ray B to travel down the entire fiber in comparison with ray A (Fig. 32–58), assuming (a) the fiber is surrounded by air, (b) the fiber is surrounded by a cylindrical glass “cladding” with index of refraction n2 = 1.460.
A ball is thrown with an initial speed v, at an angle 6, with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.
(a) the time interval during which the ball is in motion
2R
(b) the ball's speed at the peak of its path
v=
Rg 2
√ sin 26, V 3
(c) the initial vertical component of its velocity
Rg
sin ei
sin 20
(d) its initial speed
Rg
√ sin 20
×
(e) the angle 6, expressed in terms of arctan of a fraction.
1
(f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height.
hmax
R2
(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.
Xmax
R√3
2
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce.
8
(a) Assuming the ball is always thrown with the same initial speed, at what angle & should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 35.0° with no bounce (green path)?
24
(b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
Cone-bounce
no-bounce
0.940
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