6.A long core-shell structure is made to transmit an optical wave through total internal reflection within the core region. If the refractive indices for the core and the shell are respectively n₁ = 1 and n₂ = 2 as depicted in the figure, what is the maximum value of the angle θ for a successful transmission?

(A) 30°
(B) 60°
(C) 45°
(D) 90°
(E) None of the above

1.In the figure shown on the right, a wire is extended from y = -(a+L) to y = a+L and is bent as a semicircle in the xy plane. If the wire carries a current I flowing along the direction indicated by the arrows and the magnetic flux density B in the region is along the +z direction, determine the magnetic force acting on the semicircular arc with the following parameters: I = 2 A, B = 5 T, a = 1 m, L = 2 m. (A) 10 Nt (B) 20 Nt (C) 30 Nt (D) 40 Nt (E) 5 Nt

2.In free space with the permittivity of ε₀, there are two point charges of Q₁ = q and Q₂ = 6q located at (0, 2r, r) and (r, 0, 3r) in rectangular (Cartesian) coordinate system. what is the magnitude of the force experienced by Q₂?(A) (B) (C) (D) (E)

3.On the right is the cross-sectional view of a hollow and infinitely long conductor. The conductor is placed along the z axis and carries a current of 6 A in the +z direction. If the inner and the outer radii are respectively 2 cm and 4 cm (i.e. a=2 cm and b=4 cm), what is the magnitude of the magnetic field intensity at r = 3 cm? (A) 5/12π T/cm (B) 2/5π T/cm (C) 0 T/cm (D) 3/5π T/cm (E) 5/12π T/cm

4.A uniform plane wave is traveling in free space with the electric field intensity: = 12 cos(ωt + 5z) , where ω is the frequency, k is a constant, and is the unit vector in x direction. What is the propagation velocity of the wave?(A) 3×10⁸ m/s (B) 1.8×10⁹ m/s (C) -3×10⁸ m/s (D) -1.8×10⁹ ẑ m/s (E) -1.8×10⁹ m/s

5.In a perfect dielectric medium with the permeability of μ, there exists an electric field given as: = E₀ cos(ωt + kz) . What is the magnetic field (H) in the region?(A) (B) (C) (D) (E)

7.An object is placed at the position being 12 cm from a convex lens with the focal length of 10 cm. What is the possible distance between the image and the lens?(A) 5 cm (B) 10 cm (C) 15 cm (D) 20 cm (E) 25 cm

8.The spherical waves of wavelength λ emitted from a single point source are passing through two small holes, S₁ and S₂, which are separated by the distance of a, as shown in the figure. If a ＞＞ s, what is the approximated condition for destructive interference at a point P on the screen? (A) b tanθ = 1.5λ (B) a sinθ = 1.5λ (C) a sinθ = λ (D) b tanθ = λ (E) a sinθ = λ

9.A particle is strictly confined in a region of length L, but moving freely in the region. The wavefunction of the particle is shown on the right. If the total energy of the particle is 4 eV, what is its total energy when the length of the region is shrunk to be 0.5L? (A) 2 eV (B) 8 eV (C) 16 eV (D) 12 eV (E) 20 eV

10.An electron is trapped in a quantum well with the width of 10 nm, in which the first three energy states are E₁ = 3.7 meV, E₂ = 14.8 meV, and E₃ = 33.3 meV. A photon is emitted when the electron is transferred from energy level E₃ to E₂. what is the wavelength of the photon?(A) 98.12 μm (B) 111.71 μm (C) 41.89 μm (D) 27.98 μm (E) 67.03 μm

11.When a bullet, of the mass m, is fired from a gun, the speed and the location of the bullet are to be measured simultaneously. If the speed is measured with an uncertainty of Δv, what is the fundamental accuracy of the location measurement?(A) h/4mmΔv (B) h/Δv (C) h/2mΔv (D) None of the above (h is Planck's constant)

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