Light: reflection, refraction, diffraction, lenses：練習問題

A thin converging lens has a focal length of \(10\text{ cm}\). If an object is placed \(30\text{ cm}\) away from the lens, which of the following accurately describes the nature of the image formed?

A transparent oil layer of thickness \(4.5 \text{ cm}\) with a refractive index of \(1.50\) floats on a water layer of thickness \(6.65 \text{ cm}\) with a refractive index of \(1.33\). When viewed normally from above in air, what is the apparent depth of the bottom of the container?

A thin converging lens of focal length \(10\text{ cm}\) and a thin diverging lens of focal length \(20\text{ cm}\) are placed coaxially \(5\text{ cm}\) apart. An object is placed \(20\text{ cm}\) in front of the converging lens. Which of the following correctly describes the final image formed by the system?

A ray of monochromatic light travels from a transparent medium into air. If the critical angle for total internal reflection at the medium-air interface is \(30^\circ\), what is the refractive index of the medium?

An object is placed \(12\text{ cm}\) in front of a thin converging lens with a focal length of \(8\text{ cm}\). What is the linear magnification of the real image formed on a screen?

An optical lens has a focal length of \( +25 \text{ cm} \). Calculate the power of this lens in dioptres.

A ray of light traveling inside a transparent medium strikes the boundary with air at an angle of incidence equal to the critical angle of \( 41.8^\circ \), causing the refracted ray to travel along the boundary. Determine the refractive index of the medium.

A monochromatic light ray is incident from air into a transparent medium at an angle of incidence \( 60^{\circ} \). The reflected ray is found to be completely polarized, meaning it is perpendicular to the refracted ray. Calculate the wavelength of this light inside the medium if its wavelength in vacuum is \( 600 \text{ nm} \).

An object is placed \( 24.0 \text{ cm} \) in front of a thin converging lens \( L_1 \) with a focal length of \( 16.0 \text{ cm} \). A second lens, a thin diverging lens \( L_2 \) with a focal length of \( -10.0 \text{ cm} \), is placed coaxially to the right of \( L_1 \) at a distance \( d \).

(a) Calculate the position and linear magnification of the image \( I_1 \) formed by lens \( L_1 \) alone. (2 points)

(b) If the final light rays emerging from the system are parallel to the principal axis, calculate the required separation \( d \) between the two lenses. (2 points)

(c) For the arrangement in (b), determine whether the image \( I_1 \) acts as a real or virtual object for lens \( L_2 \). Briefly explain your answer. (1 point)

A glass prism has a cross-section of a right-angled triangle with angles \(30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\). The refractive index of the glass is \(n_g = 1.62\). A monochromatic light ray is incident normally on the shorter leg (the face opposite the \(30^{\circ}\) angle) of the prism.

(a) Calculate the critical angle \(c\) for the glass-air interface. (1 point)

(b) Determine the angle of incidence at the hypotenuse of the prism. Hence, explain with calculations whether the light ray undergoes total internal reflection (TIR) at the hypotenuse if it is surrounded by air. (2 points)

(c) A drop of water (\(n_w = 1.33\)) is placed on the hypotenuse at the point where the light ray strikes. Determine with reasoning if TIR still occurs at the glass-water interface. (1 point)

(d) The water is replaced by a transparent oil with a refractive index of \(n_o = 1.45\). Calculate the angle of refraction of the light ray as it enters the oil. (2 points)

(e) If the original light source is replaced by one that emits light of a shorter wavelength (e.g., violet light), state and explain how the critical angle of the glass-air interface would change. (1 point)