33. Geometric Optics

CALC FIGURE CP34.81 shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles θ₁ and θ₂ in the two media. Suppose that you did not know Snell's law. You've proven that Snell's law is equivalent to the statement that 'light traveling between two points follows the path that requires the shortest time.' This interesting way of thinking about refraction is called Fermat's principle. Write an expression for the time t it takes the light ray to travel from A to B. Your expression should be in terms of the distances a, b, and w; the variable x; and the indices of refraction n₁ and n₂.

The glass rod of Exercise 34.22 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod's axis is to be d 1.20 m inside the rod. How far from the left end of the rod must the object be located to form the image?

A laser beam in air is incident on a liquid at an angle of 53° with respect to the normal. The laser beam's angle in the liquid is 35°. What is the liquid's index of refraction?

Which of the following best describes the refraction of light and the conditions under which it occurs?

Which of the following best explains what causes the refraction of light when it passes from one medium to another?

An optical fiber consists of a core made of flint glass $n=1.66$ and cladding made of crown glass $n=1.52$. What is the critical angle for total internal reflection at the core-cladding interface?

A biologist keeps a specimen of his favorite beetle embedded in a cube of polystyrene plastic. The hapless bug appears to be 2.0 cm within the plastic. What is the beetle's actual distance beneath the surface?

A 50-year-old man uses +2.5 D lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 32 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 cm away? (Distances are measured from the lens.)

A giant ocean tank at an aquarium has acrylic plastic walls 18 cm thick. The index of refraction of acrylic plastic is 1.49. A fish is 220 cm from the inside wall. To a viewer on the outside, how far does the fish appear to be from the outside wall? Hint: The of the first refraction is the object for the second refraction.

When observing a fish underwater from above the surface, what causes the fish’s position to appear shifted from its actual location?

When a light ray passes from medium $1$ into medium $2$ and its speed increases, which of the following correctly describes the change in direction of the ray according to Snell's Law ($n_1\sin {\theta }_1=n_2\sin {\theta }_2$)?

(II) For any type of wave that reaches a boundary beyond which its speed is increased, there is a maximum incident angle if there is to be a transmitted refracted wave. This maximum incident angle θ_iM corresponds to an angle of refraction equal to 90°. If θᵢ > θ_iM, all the wave is reflected at the boundary and none is refracted, because this would correspond to sin θᵣ > 1 (where is the angle θᵣ of refraction), which is impossible.

(a) Find a formula for θ_iM using the law of refraction, Eq. 15–19.