波的性質與波動方程：练习题

A light ray travels from air into a glass block. The angle of incidence is \( 35^{\circ} \) and the angle of refraction is \( 22^{\circ} \).
What is the refractive index of the glass?

The work function of a certain metal is \( 2.30 \text{ eV} \). Calculate the threshold frequency for this metal.
(Take \( h = 6.63 \times 10^{-34} \text{ J s} \) and \( 1 \text{ eV} = 1.60 \times 10^{-19} \text{ J} \))

Light of threshold frequency \( f_0 \) is incident on a metal surface, causing the emission of photoelectrons. If the frequency of the incident light is doubled from \( f_0 \) to \( 2f_0 \), what happens to the maximum kinetic energy of the emitted photoelectrons?

A periodic wave is produced by a source vibrating at a frequency of \( 50 \text{ Hz} \). If the wavelength of the wave is \( 0.40 \text{ m} \), what is the speed of the wave?

A diffraction grating has \( 500 \) lines per millimetre. What is the grating spacing \( d \)?

A sound wave travels through air with a frequency of \( 440 \text{ Hz} \). If the speed of sound is \( 340 \text{ m s}^{-1} \), calculate the wavelength of the sound wave.

A monochromatic light source of wavelength \( 633 \text{ nm} \) is incident normally on a diffraction grating with \( 500 \) lines per mm.
Calculate the angle to the normal at which the second-order maximum is observed.

A beam of monochromatic light is incident on a boundary between air and a glass block with a refractive index of \( 1.52 \). Calculate the critical angle \( C \) for light travelling from the glass into air.

A student uses a ray box to investigate the refraction of monochromatic light as it passes from air into a rectangular glass block. The angle of incidence \( \theta_1 \) in air is varied, and the corresponding angle of refraction \( \theta_2 \) in the glass is measured.

(a) State the relationship between \( n_1 \), \( \theta_1 \), \( n_2 \), and \( \theta_2 \) at the interface.
(b) In one measurement, the angle of incidence is \( 40^{\circ} \) and the angle of refraction is \( 25^{\circ} \). Calculate the refractive index of the glass, assuming the refractive index of air is \( 1.00 \).
(c) Describe how the student could determine a more accurate value for the refractive index of the glass using a graphical method.

The photoelectric effect provides evidence for the particle nature of electromagnetic radiation. Light of frequency \( 7.5 \times 10^{14} \text{ Hz} \) is incident on a metal surface with a work function of \( 2.2 \text{ eV} \).

(a) Calculate the energy of a single photon in joules (J). (Use \( h = 6.63 \times 10^{-34} \text{ J s} \))
(b) Calculate the maximum kinetic energy of the emitted photoelectrons in electronvolts (eV). (Use \( 1 \text{ eV} = 1.60 \times 10^{-19} \text{ J} \))
(c) Explain why no photoelectrons would be emitted if the frequency of the incident light was reduced below a certain value, even if the intensity of the light was increased significantly.