33. Geometric Optics

Suppose a ray of light starts in air, then enters a slab of diamond with parallel faces, and then exits again. If the ray entered the diamond at an angle ${\theta }_{\text{i}}$ from a line normal to the diamond slab, what is true of the final angle from normal ${\theta }_{\text{f}}$ ?

Light shines from a laser in air down into water. If the laser beam in air makes an angle of $40°$ with the water's surface, what angle will it make with the surface under water?

A graduated cylinder is filled with $14\mathrm{cm}$ of oil floating on $20\mathrm{cm}$ of water. How long, in nanoseconds, does it take light to travel from the top of the oil to the bottom of the water?

A light ray, moving in air, is incident on a piece of plastic at an angle of 23° with respect to the normal. Inside the plastic the ray travels at an angle of 16° with respect to the normal. What is the index of refraction of the plastic?

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Some modern optical devices are made with glass whose index of refraction changes with distance from the front surface. FIGURE P16.72 shows the index of refraction as a function of the distance into a slab of glass of thickness L. The index of refraction increases linearly from n₁ at the front surface to n₂ at the rear surface. b. Evaluate your expression for a 1.0-cm-thick piece of glass for which n₁ = 1.50 and n₂ = 1.60.

(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 41.3° angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2° from the normal, what is the refractive index of the unknown liquid?

Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?