19. In an experiment on Newton's rings as shown in the figure, where we consider a lens of maximum thickness t and refractive index n. The radius of curvature of the spherical surface is R. When a light of wavelength A is incident from the top, the observed radius of the 3th bright fringe is given by
(A)
(B)
(C)
(D) 2Rλ/t.

15. A metal sphere of radius 2R stores an amount of charge Q initially.It then connects to another metal sphere of radius R by a conductingwire, which is removed after the charge is redistributed. Suppose the two spheres are far away apart.The ratio of the electric-field strength just outside the surface of the larger sphere to that of the smaller spheres is (A) 2:1 (B) 3:2 (C) 1:3 (D) 1:2.

16. A henry (H) is the same as (A) J/V (B) C/J (C) J/V2 (D) J/A2.

17. A negatively charged particle of mass m and charge q＜ 0 is restricted to move freely along the axis of a circular ring of radius R. A positive charge is uniformly distributed over the ring with a charge density (charge per unit length) λ＞ 0. Suppose the vertical coordinate of the particle relative to the center of the circular ring is y and y << R. Find the period of oscillation for small y: (A)2πR (B) 2πR (C) 2πR(D)πR

18. Suppose H+ and He2+ particles are injected into the device as shown in the figure from the left hole. Once they come out from the right hole, they immediately enter a region of another 9 uniform magnetic field B'perpendicular to their velocities. What is the ratio of radii of their circular motion rH+/rHe2+ under the field B'? (A) 2 (B) 1/2 (C) 1/(D) 4.

20. A Rydberg atom is an atom with one of its electrons being excited to a state of a very large principle quantum number n, called a Rydberg state. For a Rydberg hydrogen atom whose diameter is approximately 1 µm, estimate the corresponding principle quantum number n: (Hint: For the ground state, n = 1, the diameter of a hydrogen atom is approximately 1 Å.)(A) 80 (B) 100 (C) 120 (D) 140.

21. Alice is initially on the moon and takes a rocket of speed 0.8 c to the earth. How long does it take for Alice to arrive at the earth according to Alice's watch supposing the moon-to-earth distance is approximately 4 × 10⁵ km? (A) 0.01 s (B) 0.1 s (C) 1 s (D) 10 s.

22. Consider an electron contained in a one-dimensional box of size L. What is the wavelength of the emitted photon corresponding to a transition from n = 3 to n = 2?(A)(B) (C)(D)

23. Consider two inertial frames, S and S', with S' moving along the +x axis of frame S at speed v. A particle, when viewed in frame S', travels at speed u' at angle θ' to the +x direction of frame S'. The angle θ of the particle's velocity (viewed by frame S) relative to the +x axis of frame S satisfies (A) tan θ = (B) tan θ' = (C) tan θ =(D) tan θ' =

24. Which of the following statements regarding the photoelectric effect is false? (A) No electrons are emitted if the incident light falls below some cutoff frequency f₀ regardless of intensity. The cutoff frequency is characteristic of the material being illuminated. (B) Electrons are emitted almost instantaneously, even at very low light intensities. (C) As the light intensity incident on the metal is increased, the electrons should be ejected with more kinetic energy. (D) The maximum kinetic energy of the photoelectrons increases with increasing light frequency.

25. Estimate the thermal de Broglie wavelength of a hydrogen atom at 300 K: (A) 10⁻⁸ m (B) 10⁻⁹ m(C) 10⁻¹⁰ m (D) 10⁻¹¹ m.