Chapter 33: Problem 14
A ray of light traveling in water is incident on an interface with a flat piece of glass. The wavelength of the light in the water is 726 nm, and its wavelength in the glass is 544 nm. If the ray in water makes an angle of 56.0\(^\circ\) with respect to the normal to the interface, what angle does the refracted ray in the glass make with respect to the normal?
Short Answer
Step by step solution
Understand Snell's Law
Calculate the Refractive Index Using Wavelength
Solve for the Ratio of Refractive Indices
Apply Snell's Law to Find the Angle in Glass
Calculate the Angle of Refraction
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Refractive Index
- A high refractive index means light travels more slowly through the medium.
- The value is determined by comparing the speed of light in the medium to the speed of light in a vacuum, or via wavelength changes since the speed and wavelength are inversely related: the shorter the wavelength, the higher the refractive index.
Angle of Incidence
- This is the angle from where the light originates, such as the water in the exercise example.
- Angle of incidence is one of the critical factors Snell's Law uses to calculate the angle of refraction when light transfers to a different medium.
Angle of Refraction
- This angle is calculated using Snell's Law, which connects the refractive indices of the two media with the angles of incidence and refraction.
- For the light moving from water to glass in our problem, knowing the angle of refraction helps us understand the light's new direction.
Wavelength Change
- The wavelength in a medium is inversely proportional to its refractive index; as the refractive index increases, the wavelength decreases.
- In the exercise, light's wavelength changed from 726 nm in water to 544 nm in glass, meaning the light slowed down, causing the path to bend due to differing refractive indices.
Medium Transition
- This transition can lead to changes in speed, direction, and wavelength, depending on each medium's refractive index.
- Snell’s Law gives a reliable means to predict these changes by comparing the refractive indices of the two media involved.