A horizontal, parallelsided plate of glass having a refractive index of 1.52 is in contact with the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 35.0° with the normal to the top surface of the glass.(a) What angle does the ray refracted into the water make with the normal to the surface?

Verified step by step guidance

1. First, calculate the angle of refraction as the light enters the glass from air using Snell's Law, which is given by \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \). Here, \( n_1 = 1.00 \) (refractive index of air), \( \theta_1 = 35.0^\circ \) (angle of incidence), and \( n_2 = 1.52 \) (refractive index of glass). Solve for \( \theta_2 \), the angle of refraction in the glass.
2. Next, apply Snell's Law again to find the angle of refraction as the light passes from the glass into the water. Use the refractive index of water, \( n_3 = 1.33 \), and the angle \( \theta_2 \) calculated in the previous step. Set up the equation \( n_2 \sin(\theta_2) = n_3 \sin(\theta_3) \) and solve for \( \theta_3 \), the angle of refraction in the water.
3. Ensure that the angles are being calculated with respect to the normal (perpendicular to the surface). This is crucial for applying Snell's Law correctly.
4. Check if the angle of incidence at any interface leads to total internal reflection. This occurs if the angle of incidence in the denser medium is greater than the critical angle for that pair of media. The critical angle can be calculated using \( \sin(\theta_c) = \frac{n_2}{n_1} \) where \( n_1 \) is the refractive index of the less dense medium.
5. Finally, interpret the results to understand how the light ray behaves as it travels through different media with varying refractive indices, and how this affects the angle at which the ray travels in the water.

Key Concepts

Snell's Law

Snell's Law describes how light refracts when it passes from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and is equal to the ratio of the indices of refraction of the two media. Mathematically, it is expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices, and θ1 and θ2 are the angles of incidence and refraction, respectively.

Refractive Index

The refractive index is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. It is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. A higher refractive index indicates that light travels slower in that medium, which affects the bending of light rays as they enter or exit the medium.

Total Internal Reflection

Total internal reflection occurs when a light ray attempts to move from a denser medium to a less dense medium at an angle greater than the critical angle. Instead of refracting, the light is completely reflected back into the denser medium. This phenomenon is crucial in understanding how light behaves at the interface of different materials, especially in optical fibers and other applications involving light transmission.