干涉：練習題

A ray of monochromatic light travels through a glass block with a refractive index of \(1.52\) and enters a layer of water with a refractive index of \(1.33\). Calculate the critical angle \(\theta_c\) for the boundary between the glass and the water.

In a Young's double-slit experiment, monochromatic light of wavelength \(630\text{ nm}\) is incident on two slits separated by a distance of \(0.40\text{ mm}\). The interference pattern is observed on a screen placed \(2.5\text{ m}\) from the slits. Calculate the fringe spacing \(w\) on the screen.

In a Young's double-slit experiment, the slit separation is \(s\), the distance to the screen is \(D\), and the wavelength of light is \(\lambda\). If the entire apparatus is immersed in a liquid with a refractive index \(n\), what is the new fringe spacing \(w'\)?

A monochromatic light ray is incident on a boundary between a glass block and air. The refractive index of the glass is \(1.55\). If the angle of incidence within the glass is increased until it reaches the critical angle, what is the value of this angle \(\theta_c\)? (Assume the refractive index of air is \(1.00\))

A laser beam of wavelength \(532\text{ nm}\) is incident on a diffraction grating. The angle between the two second-order maxima is found to be \(64.8^\circ\). Calculate the number of lines per millimetre on the grating.

A pulse of light travels through a step-index optical fibre. The core has a refractive index of \(1.55\) and the cladding has a refractive index of \(1.48\). Calculate the critical angle \(\theta_c\) at the core–cladding interface.

A monochromatic light source of wavelength \(\lambda\) is incident on a diffraction grating with \(N\) lines per millimetre. The second-order maximum is observed at an angle \(\theta\). If the grating is replaced by one with \(2N\) lines per millimetre, explain why it might be impossible to observe a second-order maximum for the same light source.

A student uses a monochromatic laser and a diffraction grating to determine the wavelength \(\lambda\) of the light. The grating has \(400\) lines per millimetre. The laser beam is incident normally on the grating, and the resulting diffraction pattern is observed on a screen placed \(2.50\text{ m}\) from the grating.

(a) Calculate the grating spacing \(d\) in metres.
(b) The student measures the distance from the zero-order maximum to the second-order maximum on the screen to be \(1.36\text{ m}\). Calculate the angle \(\theta\) of the second-order maximum relative to the normal.
(c) Determine the wavelength \(\lambda\) of the laser light using your results from parts (a) and (b).
(d) State and explain how the distance between the zero-order and second-order maxima would change if the screen were moved further away from the grating.