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\(\bullet\) The speed of light with a wavelength of 656 \(\mathrm{nm}\) in heavy flint glass is \(1.82 \times 10^{8} \mathrm{m} / \mathrm{s} .\) What is the index of refraction of the glass at this wavelength?

Short Answer

Expert verified
The index of refraction of the glass is approximately 1.65.

Step by step solution

01

Understand the Formula for Index of Refraction

The index of refraction, often denoted by the letter 'n', can be determined by the formula \( n = \frac{c}{v} \) where \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \text{ m/s} \), and \( v \) is the speed of light in the medium.
02

Identify Given Values

From the problem, we know that the speed of light in heavy flint glass, \( v \), is \( 1.82 \times 10^8 \text{ m/s} \). The speed of light in vacuum, \( c \), is a constant \( 3 \times 10^8 \text{ m/s} \).
03

Plug Values into the Formula

Substitute the known values into the formula for the index of refraction: \[ n = \frac{3 \times 10^8 \text{ m/s}}{1.82 \times 10^8 \text{ m/s}} \].
04

Calculate the Index of Refraction

Perform the division: \( n = \frac{3}{1.82} \). Calculating this gives \( n \approx 1.65 \).
05

Review and Finalize

Ensure the calculation is correct and aligns with the physical meaning; the index of refraction is a unitless number that is a ratio of light speeds.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Speed of Light
The speed of light is a fundamental constant in physics and is denoted by the letter 'c'. In a vacuum, it travels at approximately \( 3 imes 10^8 \) meters per second. This impressive speed serves as a benchmark for measuring how light slows down when passing through various materials.
Light travels at different speeds depending on the medium it occupies, such as air, water, or glass.
This discrepancy is crucial when calculating the index of refraction, as it provides insight into how much slower light moves through a given material compared to a vacuum.
  • Standard Speed: Approximately \( 3 imes 10^8 \) m/s in a vacuum.
  • Importance: Acts as a reference point for the index of refraction.
  • Variability: Speed decreases as light enters denser materials.
Understanding the speed of light is essential to optical physics, influencing technologies like cameras, glasses, and even fiber optics.
Wavelength
Wavelength is the distance between two consecutive peaks of a wave, usually measured in nanometers (nm) for light waves.
In our exercise, we focus on light with a wavelength of 656 nm.
This parameter significantly influences how light interacts with different materials, impacting color perception and energy.
  • Definition: The length between successive wave crests.
  • Measurement: Commonly measured in nanometers.
  • Impact: Affects the speed of light in different media, as materials may scatter different wavelengths uniquely.
Different wavelengths correspond to different types of electromagnetic waves, such as radio waves, microwaves, and visible light, each playing a role in various technological applications.
Optical Physics
Optical physics is a fascinating field that studies how light behaves and interacts with matter.
It covers topics ranging from the fundamental properties of light to the complex behaviors seen in lenses and optical fibers.
Understanding these principles is vital for applications such as telescopes, microscopes, and lasers.
  • Core Focus: Investigates light's nature and manipulation.
  • Applications: Ubiquitous in scientific instruments and practical technology.
  • Importance: Drives innovation in communication, medical imaging, and more.
Through this branch of physics, we gain insights into how natural phenomena like rainbows occur and how technologies like holography are developed.
Heavy Flint Glass
Heavy flint glass is a type of optical glass known for its high refractive index and significant light dispersion.
It is commonly used in lenses where the ability to bend light dramatically is advantageous, such as in corrective glasses or camera lenses.
The higher index of refraction indicates that heavy flint glass slows down light more than many other materials.
  • Properties: High refractive index, notable dispersion.
  • Uses: Common in lenses and other optical instruments.
  • Relevance: The choice of glass affects how devices like eyeglasses and binoculars operate.
Because of these characteristics, heavy flint glass is essential in optical engineering, helping to correct aberrations and refine the focus of light in sophisticated optical systems.

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Most popular questions from this chapter

\(\bullet$$\bullet\) You (height of your eyes above the water, 1.75 \(\mathrm{m}\) ) are standing 2.00 \(\mathrm{m}\) from the edge of a 2.50 -m-deep swimming pool. You notice that you can barely see your cell phone, which went missing a few minutes before, on the bottom of the pool. How far from the side of the pool is your cell phone?

\(\bullet$$\bullet\) In a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0 ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light 21.2 ns to travel from the laser to the photocell. What is the wavelength of the light in the glass?

\(\bullet\) A light beam travels at \(1.94 \times 10^{8} \mathrm{m} / \mathrm{s}\) in quartz. The wavelength of the light in quartz is 355 \(\mathrm{nm}\) . (a) What is the index of refraction of quartz at this wavelength? (b) If this same light travels through air, what is its wavelength there?

\(\bullet\) \(\cdot\) High-energy cancer treatment. Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of \(10^{12}\) W) pulses of light that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell without causing it to explode, as long pulses would do. We can model a typical such cell as a disk 5.0\(\mu \mathrm{m}\) in diameter, with the pulse lasting for 4.0 \(\mathrm{ns}\) with an average power of \(2.0 \times 10^{12} \mathrm{W}\) . We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. (a) How much energy is given to the cell during this pulse? (b) What is the intensity (in \(\mathrm{W} / \mathrm{m}^{2} )\) delivered to the cell? (c) What are the maximum values of the electric and magnetic fields in the pulse?

\(\bullet\) Visible light. The wavelength of visible light ranges from 400 nm to 700 nm. Find the corresponding ranges of this light's (a) frequency, (b) angular frequency, (c) wave number.

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