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The human eye is most sensitive to visible light having wavelength of \(550 \mathrm{~nm}\). Express the wavenumber of this lig

Short Answer

Expert verified
The wavenumber is \(1.818 \times 10^{4} \, \text{cm}^{-1}\).

Step by step solution

01

Understand the relationship

The wavenumber is the number of wavelengths per unit distance, usually per centimeter. It is given by the formula \( \text{wavenumber} = \frac{1}{\text{wavelength}} \).
02

Convert units

Convert the wavelength from nanometers to centimeters for wavenumber calculation. Remember that \(1 \text{ nm} = 1 \times 10^{-7} \text{ cm}\). So, \(550 \text{ nm} = 550 \times 10^{-7} \text{ cm}\).
03

Calculate the wavenumber

Using the wavenumber formula, substitute the wavelength in centimeters: \[ \text{wavenumber} = \frac{1}{550 \times 10^{-7} \text{ cm}} \].
04

Simplify the calculation

Divide to find the wavenumber: \[ \text{wavenumber} = \frac{1}{550} \times 10^{7} \, \text{cm}^{-1} = 1.818 \times 10^{4} \, \text{cm}^{-1} \].

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Key Concepts

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

Visible light sensitivity
Visible light is the portion of the electromagnetic spectrum that the human eye can perceive. It ranges roughly from 380 to 750 nanometers in wavelength. Within this range, the eye is most sensitive to light at around 550 nanometers. This is because the cone cells in the retina, responsible for color vision, are optimally tuned to absorb light around this wavelength. This allows us to see most clearly and vividly in this part of the spectrum.
Understanding visible light sensitivity is crucial for applications in lighting, vision sciences, and optical technology. Knowing that 550 nm is where our eyes are most perceptive helps in designing things like energy-efficient lighting solutions and calibrators for screens and cameras.
Wavelength conversion
When working with wavelengths, it's often necessary to convert between different units of measurement. This conversion is especially important in scientific calculations, where standard units must be used to maintain consistency. In optical physics, we frequently convert wavelengths from nanometers to centimeters to derive quantities like the wavenumber.
To convert wavelengths, remember that 1 nanometer (nm) equals 1 x 10^{-7} centimeters (cm). By using this conversion factor, we can accurately translate measurements from the scale of nanometers, suitable for small light waves, to centimeters, which are more standard in scientific equations.
Nanometers to centimeters
The conversion from nanometers to centimeters is straightforward but important for calculating physical properties like the wavenumber. Since many wavelengths of light are measured in nanometers, understanding how to convert these to centimeters is essential.
  • For 1 nm, use: 1 nm = 1 x 10^{-7} cm.
  • Example: To convert 550 nm to cm, multiply: 550 nm * 1 x 10^{-7} cm/nm = 5.50 x 10^{-5} cm.

This unit conversion forms the basis for further calculations and ensures that other parameters, like the wavenumber, are computed correctly in standard scientific units.
Light wavelength
The wavelength of light plays a critical role in how light behaves and interacts with matter. Wavelengths define the color of visible light and can range significantly from shorter wavelengths like violet to longer ones like red. Light waves with different wavelengths are used in a variety of applications, from medical imaging to telecommunications.
  • Short wavelengths are more energetic and tend to penetrate materials more effectively.
  • Longer wavelengths, such as red light, are less energetic but are often used for heat-related applications.
Understanding light wavelength helps in selecting the right light source for your needs, whether that's for visual clarity or technological applications.
Optical physics
Optical physics is the study of light and its interactions with matter. It encompasses concepts such as reflection, refraction, diffraction, and wave-particle duality. These principles help explain how we perceive colors, how lenses and optical instruments work, and how light can be manipulated and harnessed.
One practical application of optical physics is calculating wavenumbers, as it allows us to quantify the spatial frequency of light waves - a key aspect in understanding light's behavior in various media. By leveraging the understanding of light's nature, optical physics paves the way for innovations in lenses, lasers, and even quantum computing.

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Most popular questions from this chapter

(a) Use Wien displacement law to determine the \(\lambda_{\max }\) of the Sun if its surface temperature is \(5800 \mathrm{~K}\). (b) The human eye sees light most efficiently if the light has a wavelength of \(5000 \AA{A}\left(1 \AA{A}=10^{-10} \mathrm{~m}\right)\), which is in the green-blue portion of the spectrum. To what blackbody temperature does that correspond? (c) Compare your answers from the first two parts and comment.

What velocity must an electron have in order to have a de Broglie wavelength of \(1.00 \AA\) Ã…? What velocity must a proton have in order to have the same de Broglie wavelength?

Lithium has a work function of \(2.90 \mathrm{eV}\). Light having a wavelength of \(1850 \AA\) is shined on Li. Determine the kinetic energy of the electron ejected.

(a) A block of wood being pushed up an inclined plar has certain forces acting on it: the force of pushing, th force of friction, the force due to gravity. Whose equatio of motion are best suited to describing this system, ar why? (b) Answer the same question but now for a rock whose velocity and altitude above ground are constant being monitored.

Human eyes detect color using cells called cones, of which there are three types based on their color sensitivity. L cones have a maximum sensitivity for light having a wavelength of \(572 \mathrm{~nm}\), while \(M\) and \(S\) cones have maxima at wavelengths of \(546 \mathrm{~nm}\) and \(430 \mathrm{~nm}\), respectively. Calculate the energies of the photons having these wavelengths.

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