Total internal reflection：練習問題

Which of the following is a necessary condition for total internal reflection to occur when a light ray hits the boundary between two transparent media?

When a light ray is incident from a dense medium (refractive index \( n_1 \)) towards a less dense medium (refractive index \( n_2 \)), and the angle of incidence is exactly equal to the critical angle, what is the path of the light ray?

A ray of light is incident perpendicularly on the face AB of a right-angled isosceles prism ABC (\(n = 1.50\)). The ray then hits the hypotenuse face AC. If the prism is placed in a transparent liquid with a refractive index of \(1.30\), what will happen to the ray at face AC?

(Note: \(\sin 45^\circ \approx 0.707\); \(\sin 60^\circ \approx 0.866\))

What is the critical angle for a material-air interface?

In a laboratory experiment, a light ray is directed from a transparent plastic block into the air. A student observes that the refracted ray gradually moves closer to the interface as the angle of incidence increases, and eventually disappears when the angle of incidence reaches exactly \(38.0^\circ\). What is the refractive index of the plastic block?

Explain why a diamond sparkles much more than a piece of glass of the same shape, referring to the concept of total internal reflection.

A light ray travels from a transparent liquid with a refractive index of \(n = 1.42\) towards the boundary with air. Calculate the critical angle for this liquid-air interface and state what happens to the ray if the angle of incidence is exactly \(45^\circ\).

In a periscope using two \(45^\circ\)-\(90^\circ\)-\(45^\circ\) glass prisms (\(n = 1.50\)), light reflects off the internal hypotenuse. If the prism is accidentally submerged in a liquid with a refractive index of \(1.45\), explain why the periscope will fail to show an image, supporting your answer with a comparison of angles.

Light travels from an optically denser medium to an optically less dense medium.

(a) What is the critical angle?

(b) Describe the condition under which a light ray will undergo total internal reflection.

A ray of light is travelling inside a transparent plastic block with a refractive index of \( n = 1.62 \) towards a boundary with an unknown liquid. It is observed that the critical angle for this plastic-liquid interface is exactly \( 55.0^\circ \).

(a) Calculate the refractive index of the unknown liquid. (2 points)
(b) If the liquid is replaced by air (refractive index \( n = 1.00 \)), explain whether the critical angle will increase, decrease, or stay the same. Show your reasoning using the relationship between the refractive index and the critical angle. (2 points)