Refraction at a plane surface：練習問題

Monochromatic light of wavelength \(550 \text{ nm}\) in a vacuum enters a block of transparent material with a refractive index of \(1.50\). If the speed of light in a vacuum is \(3.00 \times 10^8 \text{ m s}^{-1}\), calculate the wavelength of the light within the transparent material.

An optical signal consisting of short pulses of light is transmitted along a long step-index optical fibre. Which combination of factors correctly describes a source of pulse broadening and its resulting effect on data transmission rate?

A ray of light travels from water (refractive index \(n_1 = 1.33\)) into glass (refractive index \(n_2 = 1.50\)). If the angle of incidence in the water is \(35.0^\circ\), what is the angle of refraction in the glass?

A point source of light is located \(5.0 \text{ cm}\) below the surface of a liquid. The light ray that reaches the surface at the critical angle \(\theta_c\) illuminates a circle of radius \(R = 6.0 \text{ cm}\) on the surface, centered directly above the source. Calculate the refractive index, \(n\), of the liquid.

A coin is placed at the bottom of a container of liquid. The real depth of the coin is \(12.0 \text{ cm}\). If the refractive index of the liquid is \(1.40\), what is the apparent depth of the coin when viewed normally from above?

The refractive index of diamond is approximately 2.42. Given that the speed of light in a vacuum is \(c = 3.00 \times 10^8 \text{ m/s}\), calculate the speed of light in diamond.

An optical fibre core has \(n_{core} = 1.50\) and cladding has \(n_{clad} = 1.48\). Calculate the maximum angle of incidence in air (\(n_{air} = 1.00\)) for a ray entering the fibre such that it is subsequently contained by total internal reflection.

Light is incident from a block of glass, which has a refractive index of 1.50, into air (refractive index 1.00). Calculate the critical angle, \(\theta_c\), for which total internal reflection first occurs at the glass-air boundary.

Optical fibres rely on the principle of total internal reflection (TIR) to transmit data efficiently over long distances.

(a) An optical fibre consists of a core and surrounding cladding. Explain why the core must have a higher refractive index than the cladding, and state the condition necessary for TIR to occur at the core-cladding boundary.

(b) High-speed digital communication uses short pulses of light. Explain the phenomenon of modal dispersion in a step-index optical fibre and describe how it affects the maximum data transmission rate.

A tank contains a layer of water (refractive index \(n_w = 1.33\)) above a dense transparent liquid X (refractive index \(n_x = 1.60\)). A light source is placed at the bottom, in liquid X. A ray of light from the source strikes the boundary between liquid X and water at an angle of incidence \(\theta_i\).

(a) Calculate the critical angle, \(\theta_{c, XW}\), for total internal reflection (TIR) at the boundary between liquid X and water.

(b) If the angle of incidence is \(\theta_i = 35.0^\circ\), calculate the angle of refraction in the water layer, \(\theta_r\).

(c) This refracted ray strikes the water-air boundary (refractive index of air \(n_a = 1.00\)). Calculate the critical angle for the water-air boundary, \(\theta_{c, WA}\).

(d) If the angle of incidence at the water-air boundary is the angle calculated in part (b), determine whether the light ray will emerge into the air or undergo TIR. Justify your answer.