10. 如圖，真空中有一玻璃製橢球體長軸 10cm、短軸 8cm，若 以平行於長軸之光線射向此橢球體，發現折射後的光線恰可通過橢球內的後方焦點上，則此玻璃之折射率為何？

1. As shown in Figure (1), space shuttle travels in a circular orbit 2R above the surface of the Earth with a period of T, where R is the radius of the Earth. The shuttle is now returning to the ground from point A of the orbit, it must reduce the speed at point A and enters a new elliptical orbit with the center of the Earth at one focus, and the orbit is tangent to the Earth's surface at point B. AB is the major axis of the ellipse. How long does it take for the shuttle to land from point A to the ground (point B)? In terms of T.

2. As shown in Figure (2), two identical blocks B and C of length 36.0 cm on the smooth horizontal surface, and the object A(treat A as a particle) is located at the right end of B, with the same mass of A, B and C. A and B are moving with the same speed toward the stationary C, and then B undergoes a one-dimensional completely inelastic collision with C. A is known to slide to the right end of C without falling and there is friction between A and C. Find the distance that C has traveled from the collision of B and C to A just arriving the right end of C.

3. Figure (3) shows the transverse velocity u versus time t of the point on a string at x = 0, as a wave passes through it. If the wave has the form y(x, t) = ym sin(kx - ωt - ϕ). What is the phase constant ϕ?

4. Pipe A has only one open end; pipe B is four times as long and has two open ends. Of the lowest 10 harmonic numbers nB of pipe B, what is the second smallest value at which a harmonic frequency of B matches one of the harmonic frequencies of A ?

5. A small lightbulb suspended at distance d1 = 250 cm above the surface of the water in a swimming pool where the water depth is d2 = 200 cm. The bottom of the pool is a large mirror. Looking down nearly perpendicularly, how far below the real mirror surface is the image of the bulb?

6. A particle of charge +Q is assumed to have a fixed position at P. A second particle of mass m and charge –Q moves at constant speed in a circle of radius R1, centered at P. Derive an expression for the work that must be done by an external agent on the second particle in order to increase the radius of the circle of motion, centered at P, to R2.

7. In Figure (4), a voltmeter of resistance Rv = 300 Ω and an ammeter of resistance RA = 5.00 Ω are being used to measure a resistance R in a circuit that also contains a resistance R0 = 100 Ω and an ideal battery of emf ε = 18.0 V. Resistance R is given by R = V/i, where V is the voltmeter reading and i is the current in resistance R. However, the ammeter reading is not i but rather i'. Thus, the ratio of the two meter readings is not R but only an apparent resistance R' = V/i'. Assume that R = 100 Ω. Calculate the apparent resistance R' ?

8. X rays with wavelength λ = 1.24 Å eject photoelectrons from a gold foil. The electrons form circular paths of radius r in a region of magnetic field B. Experiment shows that rB = 1.82×10-4 tesla-m. Find the work function of the gold foil in electron volts. ( Electron rest mass me = 9.1×10-31 kg )

9. Radiation from a helium ion He+ is nearly equal in wavelength to the first line of the Balmer series. Between what states (values of n) does the transition in the helium ion occur?

10.In Figure (5), a wheel of radius 0.25 m is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a 2.0 kg box that slides on a frictionless surface inclined at angle θ = 37° with the horizontal. The box accelerates down the surface at 2.5 m/s2 . What is the rotational inertia of the wheel about the axle? (g = 10 m/s2 )

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