Physics of vision and hearing：練習問題

Which of the following statements correctly describes the properties of rods and cones in the human retina?

When a person with normal vision shifts their gaze from a distant object to a near object at their near point, which of the following describes the change in the state of the eye?

The Rayleigh criterion states that the minimum resolvable angular separation is \(\theta \approx \frac{1.22\lambda}{d}\). If a diver is observing two underwater LEDs using light of wavelength \(540 \text{ nm}\) (in vacuum), how does the angular resolution of the eye change compared to when observing in air? (Assume the refractive index of water is \(1.33\) and the pupil diameter remains constant).

A lens is used to correct a vision defect and has a focal length of \(+50 \text{ cm}\). What is the power of this lens?

Two identical sound sources are playing simultaneously. If a single source produces a sound intensity level of \(55 \text{ dB}\) at a certain point, what is the total sound intensity level when both sources are turned on?

Explain why a logarithmic scale is used to represent the sound intensity level in decibels when describing the human perception of sound.

If a person moves away from a sound source such that the sound intensity decreases to exactly one-third of its original value, calculate the change in the sound intensity level in \(\text{dB}\).

The human middle ear enhances pressure to compensate for the impedance mismatch between air and the fluid in the inner ear. If the effective area ratio between the eardrum and the oval window is \(17.5:1\) and the ossicular lever system provides a mechanical advantage of \(1.35\), calculate the gain in sound intensity level (in \(\text{dB}\)) at the oval window. Assume sound intensity \(I\) is proportional to the square of the pressure \(p\).

(a) Explain how the middle ear provides pressure amplification between the eardrum and the oval window. Mention at least two physical mechanisms involved.

(b) The sound intensity level at a construction site is measured to be \(90 \text{ dB}\). Given that the reference intensity \(I_0 = 1.0 \times 10^{-12} \text{ W m}^{-2}\), calculate the sound intensity \(I\) at this site.

(c) If the construction worker puts on ear protectors that reduce the sound intensity by a factor of \(50\), calculate the new sound intensity level experienced by the worker.

A person is diagnosed with a vision defect where their far point is located at \(0.50 \text{ m}\) from the eye. They wish to use spectacles to see distant objects clearly.

(a) Identify the vision defect and state the type of lens (converging or diverging) needed for correction. (1 point)

(b) Calculate the power of the required lens in dioptres. (2 points)

(c) The human ear acts as a transducer and pressure amplifier. Describe how the area ratio between the eardrum and the oval window, along with the lever action of the ossicles, contributes to pressure amplification in the middle ear. (2 points)