Refraction of Light & Snell's Law Practice Problems

Consider a person placing a 1.5 cm-thick vegetable oil layer on a horizontal glass surface. A laser beam in the air strikes the oil at 40° from normal. What direction, measured as an angle from normal, does the laser beam travel when it enters the glass? (Assume the refractive index of oil is 1.47 and for glass is 1.50).

A scientist conducts an experiment to determine the refractive index of a transparent optical cylinder. A diode laser beam with a wavelength of 980 nm in the air is directed through the cylinder and travels a distance of 1.25 m in 6.45 ns. Using this data, calculate the wavelength of the laser inside the cylinder.

A linear gradient refractive index (linear GRIN) is a type of GRIN material where the refractive index changes linearly with distance. Suppose that the refractive index of a linear GRIN increases at a constant rate between 1.48 (point A) and 1.56 (point B). A and B lie on the horizontal axis and the distance separating points A and B is 3.5 cm. Calculate the time needed for an electromagnetic wave to travel between points A and B.

A tourist drops a coin vertically into a wishing well of height 80.0 cm that is totally filled with a liquid of refractive index n. The coin lands 26.0 cm from the well's border. However, when the tourist looks in from the same border, the coin appears 38.0 cm from the well's border. Determine n.

A researcher is investigating a solution in a petri dish. They shine a beam of light at a 55° angle to the normal from the air onto the solution. The beam refracts inside the solution and continues at a 37° angle to the normal. Determine the solution's refractive index.

Consider a ruby cube with a refractive index 1.76 dropped into a water pool. A light beam in the water hits the ruby surface at an incidence angle of 30°. Determine the beam's angle relative to the ruby's surface after entering the crystal.

An underwater archaeologist explores a shipwreck at night and observes the moon 45° above the horizontal line of sight. What is the moon's height above the horizon for a person standing on a surfboard directly above the archaeologist?

A photographer captured a stunning moment by encapsulating a fragile butterfly within a transparent plastic cube. The butterfly was observed within the plastic surface at a distance of 4.0 cm. If the index of refraction of plastic for overhead viewing is 1.60, determine the actual distance of the butterfly beneath the surface.

Consider a lobster in a glass tank. The actual thickness of the tank's glass walls is 3.00 mm, but to the lobster inside, it appears 2.50 mm thick. Calculate the refraction index of the glass material.

A greenhouse uses glass panes with a thickness of 3.0 mm. The index of refraction of glass is about 1.52. A scientist is observing a plant that is 100.0 cm away from the inside of the glass. To an observer outside the greenhouse, how far does the plant appear to be from the outside of the glass pane?

Consider a serene lake surface being hit by a ray of sunlight. If the refractive index of the water is symbolized by 'n', find the angle at which the sunlight strikes the surface such that the resulting angle of refraction inside the water is double that of the original angle of incidence.

A cylindrical glass container with a diameter of 40 cm and a height of 60 cm is filled entirely with olive oil (n = 1.47). The container has etchings every 5 cm along the inside of the glass, starting from the top (0 cm) and ending at the bottom (60 cm). You stand on the other side of the container, with your eye line matching the oil's surface. Can you see the etchings from the top (0 cm) going downwards, or from the bottom (60 cm) going upwards? Justify your answer. Note: The index of refraction of air is n = 1.0

In a biomedical lab, researchers use a visible light microscope to analyze samples. The light from the microscope travels through the sample and back to a detector. The detector processes the received light in 1.5 ns. If the information must be obtained from the sample within 2.0 ns, what is the maximum thickness of the sample? The sample is embedded in a medium with an index of refraction of 1.4.

In a submarine exhibit, a 0.8 m submarine prototype is witnessed moving into a vast water tank at a speed of 1.3 m/s as perceived by an observer. The observer sees the submarine coming directly toward him from behind the tank's glass wall. Determine the submarine's true speed in the water. Assume that the thickness of the glass does not affect the perceived motion of the submarine.

A beam of sunlight strikes a right triangle prism, as shown in the figure below. The incident angle of the beam on side BC of the prism is 60°. The blue light exits side AB parallel to the normal of side AB. Given that the refractive index for yellow in this type of glass is 3.5% higher than that of blue, calculate the angular deviation between the yellow light and the blue light exiting the prism.

Flint glass has a refractive index between (1.45 and 2.00) and is surrounded by air. A narrow beam of white light strikes the vertically placed piece of flint glass at an angle of 62° with the normal in air. What should be the angular separation between the yellow (550nm) and red color (700nm) in the refracted ray? When n_R = 1.42 and n_Y = 1.44 in flint glass.

A flat slab of fused quartz is struck by a incoming ray of light that is initially traveling in the air at an angle of incidence of 63.0°. Green light will form at an angle of 34.1° and yellow light will form an angle of 39.5° that is normal to the slab. Determine what the speeds of the green and yellow light will be which are formed from this light ray striking the slab.

A child is sitting on a tree branch that reaches across the river and is 6 m above the river's surface. While on the top, he spots a shopping trolly at the bottom of the river right below him. The distance between him and the trolly looks to be 15m.  Find how deep the water is. The water's surface is like a spherical surface with an infinite radius of curvature.

A blue light ray propagates in a transparent methanol liquid with a refractive index of 1.33. The wavelength of blue light in a vacuum is 455 nm. Determine the wavelength of the blue light in methanol.

The wavelength of a laser beam in fluorite is 615 nm. The laser beam propagates in fluorite at a speed of 2.09 ×10⁸ m/s. Find the wavelength of this light wave once it emerges into the air..

A monochromatic beam of light of frequency f is split into two beams. The first beam has a wavelength of 450 nm in a quartz medium with a refractive index of 1.50. The second beam enters an ethanol medium. The refractive index of ethanol is 1.36. Determine the wavelength of this light in ethanol.

A light ray strikes a boundary between air and polystyrene at an angle of 50.0° with the normal. The refracted ray is transmitted into polystyrene and makes an angle of 31.0° with the normal. Determine the speed of propagation of light in polystyrene.

A quartz cuvette is filled with turpentine oil. The refractive indices of quartz and turpentine oil are 1.54 and 1.47, respectively. The side thickness of the cuvette is 1.25 mm. A laser beam strikes the cuvette side at an angle of 35° with respect to the normal to the cuvette surface. The refracted beam in turpentine is θ with respect to the cuvette surface. i) Determine θ. The experiment is repeated with the same angle of incidence on the cuvette side, now filled with an unknown transparent liquid. The refracted beam in the liquid forms an angle of 25° with respect to the normal to the cuvette surface. ii) Determine the index of refraction (n_liquid) of the unknown medium.

Assume a transparent cylinder of radius R = 4.0 cm made of crown glass with an index of refraction of 1.52. The cylinder lies entirely on the bottom of a container filled with water (n_Water = 1.33). The boundary between the crown glass and water is a convex hemispherical surface with a radius of 1.5 cm. An object located to the left of the hemispherical surface forms an image on the cylinder axis, 60 cm inside the cylinder. Determine the position of the object from the hemispherical surface.

A light beam in the air strikes a flat layer of pure quartz of thickness t placed in contact with a thick layer of turpentine oil. The beam is incident on the air-quartz interface at an angle of 28° with respect to the normal to the surface and emerges at angle θ_r in the turpentine. Determine θ_r. The refractive indices of quartz and turpentine are 1.54 and 1.47 respectively.

Sunlight radiations encounter gas molecules in the earth's atmosphere, and a scattering phenomenon occurs. The gas molecule scatters violet light (350 nm) in all directions with an intensity of I_violet, while red light (600 nm) is scattered with an intensity of I_red. Determine the ratio of I_red to I_violet.

A light ray is incident on a series of two solid slabs, as shown in the figure. The first slab has an index of refraction of 1.53, and the second slab has an index of refraction of 1.47. The light emerges out of the second slab into the air, forming an angle θ_r with the normal to the surface. Determine θ_r by exploiting the data given in the figure.

A rectangular transparent glass filled with liquid of refractive index 1.41 has equal width and length dimensions, both measuring 1.0 m. When a beam of parallel light strikes the aquarium at an angle of 29.7°, no light reaches the bottom. Calculate h, the height of the aquarium.

The figure below shows an overhead view of a monochromatic light hitting the surface of a transparent polymer with a refractive index of 1.39. The device emitting the light is placed at L( 12 cm, 0 cm) and the light hits the polymer at I ( 0 cm, 6.7 cm). What will happen to the light at the surface AB?

A beam of light traveling vertically downward is incident on a triangular glass prism of refractive index 1.52, as shown in the figure below. Determine the angle of deviation of the light as it exits the prism relative to its initial vertical direction.

When a beam of white light passes through a transparent medium, it disperses into a spectrum of colors due to the varying refractive indices of different wavelengths. Consider a beam of light that is incident on a microscope slide with an angle of 20°. It is observed that the wavelength λ _R (630 nm), having a refractive index n _R (1.576), is refracted at an angle θ _R. The wavelength λ _B (470 nm), having a refractive index n _B, is refracted at an angle θ _R - 0.32°. Calculate n _B. Hint: When the refractive index varies by δn (δn<<n) due to the wavelength variation, the angle of refraction varies by δθ.

A beam of white light is incident perpendicularly to the face of a right triangular prism made of transparent ice. The angle between the entering face and the hypotenuse, where the light exits, is 40°. Calculate the angular dispersion between violet and orange light as they exit the prism. Assume that the refractive indices for violet and orange light in ice are 1.331 and 1.317, respectively.

During an optics experiment, a ray of light in a vacuum strikes a diamond surface (n = 2.42). You notice that the angle at which the light reflects off the surface is three times the angle at which it refracts into the diamond. What is the angle at which the light initially strikes the diamond?

A diver shines a flashlight toward the surface of a lake, and the light exits the water at an angle of refraction equal to 45° from the normal line. What was the original angle at which it hit the water-air interface?

A beam of light travels from a vacuum into a glass slab at an incident angle of 15° with respect to the normal line at the glass surface. Given the refractive indices of the materials, where n _vacuum = 1.0 and n _glass = 1.5. Calculate the angle of refraction inside the glass.

In a specific liquid, light travels at a speed that is two-thirds the speed of light in glass. What is the refractive index of this liquid if the refractive index of glass (n _glass​) is 1.5?

As a physicist, you need to measure the speed of light in three materials: water, diamond, and flint glass. Since light travels at 3.00 × 10⁸ m/s in a vacuum, can you calculate its speed in the given substances?[Hint: n_water = 1.33, n_diamond = 2.42, n_{flint glass} = 1.62]

You are a researcher studying the optical properties of diamonds. You measure the speed of light in a diamond to be 1.24 × 10⁸ m/s, while the speed of light in a vacuum is 3.00 × 10⁸ m/s. What is the index of refraction of diamonds?

A vat that is 2.0 m high and 2.0 m wide houses a 1.2-m-long glass rod. This rod is placed horizontally, positioned at the center of the vat's bottom. You decide to observe from a point just above the edge of the vat, looking along the direction of the rod. Calculate the angle you could observe between the two ends of the rod under two conditions: (i) when the vat is empty, assuming air is the medium, and (ii) when the vat is completely filled with ethanol, which has a refractive index of 1.36.