Chapter 33: Problem 47
A thin layer of ice (\(n\) = 1.309) floats on the surface of water (\(n\) = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. (a) What is the largest angle with respect to the normal that the ray can make at the ice-water interface and still pass out into the air above the ice? (b) What is this angle after the ice melts?
Short Answer
Step by step solution
Understand the Concept
Determine the Interface
Use Snell's Law
Calculate Critical Angle at Ice-Water Interface Before Melting
Calculate Critical Angle at Ice-Air Interface
Determine the Largest Angle Before Ice Melts
Angle After Ice Melts
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Snell's Law
One practical application of Snell's Law is in calculating the critical angle for total internal reflection, a crucial concept in optics. For a ray traveling from a denser medium to a less dense one, if it hits the boundary at an angle greater than this critical angle, it will not pass through but instead reflect back into the denser medium.
- The denser medium has a higher refractive index (\(n\)).
- Total internal reflection occurs when \(\theta_2\) is 90 degrees, making the refracted ray skim along the boundary.
Total Internal Reflection
The critical angle is key to understanding total internal reflection. It is the maximum angle of incidence in the denser medium beyond which the light cannot refract into the less dense medium. Instead, it is entirely reflected back inside. This happening is not just a peculiarity; it is widely used in designing instruments like fiber optics, binoculars, and even periscopes.
- The critical angle depends on the refractive indices of the two media in contact.
- If the incident angle is greater than the critical angle, the light doesn't escape.
Refraction of Light
When light enters a denser medium (e.g., from air to water), it slows down and bends towards the normal – an imaginary line perpendicular to the surface at the point of incidence. Conversely, transitioning into a less dense medium causes the ray to speed up and bend away from the normal. Snell's Law helps calculate this bending precisely using the media's refractive indices.
- Bending is more pronounced with larger differences in refractive indices.
- Light waves are generally fastest in vacuum and slowest in solid materials.