(II) An aquarium filled with water has flat glass sides whose index of refraction is 1.51. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. 32–52). What is the angle of this light ray when it enters (a) the glass, and then (b) the water? (c) What would be the refracted angle if the ray entered the water directly?

Verified step by step guidance

1. Step 1: Identify the given values and the laws of refraction to be used. The index of refraction of the glass is \( n_{glass} = 1.51 \), the angle of incidence in air is \( \theta_{air} = 43.5^{\circ} \), and the index of refraction of air is \( n_{air} = 1.00 \). Use Snell's Law, which states \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \), to calculate the angle of refraction when the light enters the glass.
2. Step 2: Apply Snell's Law for part (a). Substitute \( n_{air} \), \( \theta_{air} \), and \( n_{glass} \) into the equation \( n_{air} \sin(\theta_{air}) = n_{glass} \sin(\theta_{glass}) \). Solve for \( \sin(\theta_{glass}) \) and then find \( \theta_{glass} \) using the inverse sine function.
3. Step 3: For part (b), consider the transition of the light ray from the glass into the water. The index of refraction of water is \( n_{water} = 1.33 \). Use Snell's Law again, \( n_{glass} \sin(\theta_{glass}) = n_{water} \sin(\theta_{water}) \), to calculate the angle of refraction \( \theta_{water} \). Substitute the previously calculated \( \theta_{glass} \) and solve for \( \theta_{water} \).
4. Step 4: For part (c), consider the scenario where the light ray enters the water directly from the air. Use Snell's Law again, \( n_{air} \sin(\theta_{air}) = n_{water} \sin(\theta_{water\_direct}) \). Substitute \( n_{air} \), \( \theta_{air} \), and \( n_{water} \) to solve for \( \sin(\theta_{water\_direct}) \), and then find \( \theta_{water\_direct} \) using the inverse sine function.
5. Step 5: Summarize the results conceptually. The angles of refraction depend on the indices of refraction of the materials and the angle of incidence. The light bends towards the normal when entering a medium with a higher index of refraction and away from the normal when entering a medium with a lower index of refraction. This behavior is governed by Snell's Law.

Key Concepts

Refraction

Refraction is the bending of light as it passes from one medium to another with a different index of refraction. This phenomenon occurs because light travels at different speeds in different materials. The degree of bending is described by Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media.

Snell's Law

Snell's Law provides a mathematical relationship to determine the angle of refraction when light transitions between two media. It is expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the indices of refraction of the first and second media, respectively, and θ1 and θ2 are the angles of incidence and refraction. This law is essential for calculating how much a light ray bends when entering or exiting different materials.

Index of Refraction

The index of refraction is a dimensionless number that describes how much light slows down in a medium compared to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. A higher index indicates that light travels slower in that medium, which affects the angle of refraction when light enters or exits the material.