Question

The normal human eye responds to visible light of wavelength raging from about 390 to 710 nm. Determine the frequency range of the human eye.

Answer 1

A typical human eye will respond to wavelengths from 390 to 700 nm (in vacuum or air). In terms of frequency this corresponds to a band in the vicinity of 430–790 THz.

Answer 2

Answer:

Concept:

The fundamental characteristics of wavelengths are frequency, wavelength, and photon intensity, and they are all interrelated. Wavelengths between 390 and 700 nm are responsive to the average human eye (vacuum or air). A range between 430 and 790 THz often surrounds this. A photon's energy (E) is equal to a frequency multiplied by h, where h is Planck's constant.

Given:

Wavelength = 390 to 710 nm

To Find:

Frequency range of the human eye = ?

Solution:

Step 1:

Speed of light=3×$10^{8}$ $\frac{m}{s}$

v = f $\lambda$

Step 2:

Lower limit of frequency range of visible light corresponding to $\lambda$=710 nm

= 7.1×$10^{-7}$

fL= $\frac{3\times 10^{8}}{7.1 \times 10^{-7} }$

fL = $(4.225\times 10^{14})$hz

Step 3:

Upper limit of frequency range of visible light corresponding to $\lambda$=390nm

=$3.9 \times 10^{-7}$

fU=$\frac{3\times 10^{8}}{3.9\times 10^{-7}}$

fU= $(7.69\times 10^{14})$hz

Result:

Frequency ranges from $(4.225\times 10^{14})$ hz to $(7.69\times 10^{14})$ hz

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