C.3 波的現象：練習題

Unpolarized light of intensity \( I_0 \) is incident on an ideal linear polarizer. What is the intensity of the light transmitted through the polarizer?

In a Young's double-slit experiment, the fringe separation is \( s \) when light of wavelength \( 400 \text{ nm} \) is used. If the wavelength is changed to \( 600 \text{ nm} \) and the distance between the slits is halved, what is the new fringe separation?

In a Young's double-slit experiment, a fringe separation \(s\) is observed on a screen. The distance between the slits is then doubled, the distance from the slits to the screen is tripled, and the wavelength of the light is halved. What is the new fringe separation?

According to the Rayleigh criterion, two point sources are just resolved by an optical instrument when the central maximum of the diffraction pattern of one source coincides with which point of the diffraction pattern of the other source?

Two coherent sources of light are in phase and emit waves of wavelength \(\lambda\). What is the minimum non-zero path difference between the waves at a point where destructive interference occurs?

State the effect on the width of the central maximum in a single-slit diffraction pattern when the width of the slit is decreased while keeping the wavelength of light constant.

Light enters a glass block from air at an angle of incidence of \(40^\circ\). If the refractive index of the glass is \(1.52\), calculate the angle of refraction inside the block.

Monochromatic light is incident on two slits separated by \(0.20 \text{ mm}\). A screen is placed \(1.5 \text{ m}\) away and the distance between the central maximum and the first bright fringe is \(4.5 \text{ mm}\). Calculate the wavelength of the light.

Unpolarized light of intensity \(I_0\) is incident on a vertical polarizing filter. The light then passes through a second polarizing filter whose transmission axis is at an angle of \(60^{\circ}\) to the vertical.
(a) State the intensity of the light after passing through the first filter in terms of \(I_0\).
(b) State Malus's Law and identify the variables used in the equation.
(c) Calculate the intensity of the light emerging from the second filter in terms of \(I_0\).
(d) Describe how the transmitted intensity changes as the second filter is rotated through a total of \(180^{\circ}\) starting from the vertical position.

A thin film of oil with a refractive index of 1.45 floats on water (refractive index 1.33). White light is incident normally on the film.
(a) Explain why a phase change of \(\pi\) occurs at the air-oil interface but not at the oil-water interface.
(b) Calculate the minimum non-zero thickness of the oil film that will result in destructive interference for reflected light of wavelength 580 nm.
(c) If the oil film thickness is gradually increased, describe the change in the observed color of the reflected light.