Question

The index of refraction of the vitreous humor is greater than the index of refraction of the aqueous humor which is greater than the index of refraction of air. What is the relationship of the speed of light in each of these media? 1\. Fastest in air, slower in aqueous humor, slowest in vitreous humor 2\. Fastest in vitreous humor, slower in aqueous humor, slowest in air 3\. Equal in all three 4\. Depends on the index of refraction of the lenses which separate the media

Short answer

The speed of light in the given media is fastest in air, slower in aqueous humor, and slowest in vitreous humor. This relationship is due to the inverse proportion between the index of refraction and the speed of light in a medium.

Step-by-step solution

Snell's Law and Index of Refraction

Snell's Law states that the index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a medium. The formula is given by: n = $\frac{c}{v}$ where: n = index of refraction c = speed of light in a vacuum v = speed of light in the medium From Snell's Law, we understand that as the index of refraction increases, the speed of light in the medium decreases.

Compare Index of Refraction of Media

We are given that the index of refraction of vitreous humor is greater than the index of refraction of aqueous humor, which is greater than the index of refraction of air. We can write this as: $n_{vitreous}>n_{aqueous}>n_{air}$

Apply Snell's Law to Find the Relationship

Using the information from Snell's Law, we know that the speed of light in a medium is inversely proportional to its index of refraction. Since $n_{vitreous}>n_{aqueous}>n_{air}$, and the speed of light is inversely proportional to the index of refraction, we can determine the relationship between the speed of light in these media: $v_{air}>v_{aqueous}>v_{vitreous}$ The speed of light is fastest in air, slower in aqueous humor, and slowest in vitreous humor. Therefore, the correct answer is: 1. Fastest in air, slower in aqueous humor, slowest in vitreous humor

Key concepts

Index of Refraction

The index of refraction is an important concept in optics that helps us understand how light behaves when it moves from one medium to another. It is defined as the ratio of the speed of light in a vacuum to the speed of light in a particular medium. This is represented by the formula:$$n=\frac{c}{v}$$Here:

• $n$: Index of refraction
• $c$: Speed of light in a vacuum (approximately $3\times {10}^8$ meters per second)
• $v$: Speed of light in the medium

The index of refraction tells us how much the light slows down when it enters a medium. A higher index means that the light travels more slowly through that medium. This slowing down is what causes light to bend when it passes through different substances, a phenomenon known as refraction. If you ever watched a straw in a glass of water appear bent, you've witnessed refraction in action! The more dense the medium, in terms of optical density, the higher its index of refraction, causing a more significant bending of light.

Speed of Light

The speed of light is a fundamental constant that plays a crucial role in many areas of physics. In a vacuum, light travels at approximately 299,792,458 meters per second, often rounded to $3\times {10}^8$ m/s. However, when light enters a medium such as air, water, or glass, it interacts with the particles in that medium and slows down.This speed reduction is directly related to the medium's index of refraction. Different mediums have different effects on the speed of light, depending on their optical density. For example:

• Air, with a low index of refraction, allows light to travel almost as fast as in a vacuum.
• Water, with a higher index, slows light down more than air.
• Glass or other denser substances slow light down even further.

Understanding how light slows in various media is vital for numerous practical applications, from designing lenses and glasses to understanding natural phenomena like rainbows. It's fascinating to see how much our everyday experiences are shaped by this simple concept of light speed variation.

Optics Education

Optics education introduces students to the fascinating world of light and its properties, including refraction, reflection, and dispersion. One foundational concept taught in optics is Snell's Law, which describes how light behaves as it travels through different media. Understanding Snell's Law gives students insight into practical applications such as cameras, spectacles, and microscopes, which all rely on the bending of light. In the classroom, students learn about:

• The basic principles of light behavior.
• How the index of refraction influences the path of light.
• The mathematical relationships governing light speed in different materials.

Engaging with optics helps develop analytical and problem-solving skills. By exploring real-world problems, like calculating the refraction using Snell's Law, students see the direct application of abstract concepts. This helps bridge the gap between theory and practice, making learning both effective and enjoyable. Optics education is not only about learning scientific concepts but also about understanding the world and its many intricate behaviors through the lens of light.