Visible light has wavelengths ranging from 400 nm (violet) to 750 nm (red). Express these wavelengths in terms of frequency (Hz).

Question

Visible light has wavelengths ranging from 400 nm (violet) to 750 nm (red). Express these wavelengths in terms of frequency (Hz). (1 nm = 10^-9m)

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Given :

Wavelengths :

λ₁ = 400 nm (for violet light),

λ₂ = 750 nm (for red light)

To find :

Frequencies : ν₁, ν₂

Formula :

ν = \(\frac{c}{\lambda}\)

Calculation :

i. Wavelength of violet light,

λ₁ = 400 nm = 400 × 10^-9 m

Frequency,

ν = \(\frac{c}{\lambda}\)

Where c is speed of light = 3.0 × 10⁸ms^-1

∴ ν₁ = \(\frac{3.0\times 10^8 ms^{-1}}{400\times 10^{-9}m}\)

= 7.50 × 10¹⁴Hz

ii. Wavelength of red light,

λ₂ = 750 nm = 750 × 10^-9m

Frequency,

ν = \(\frac{c}{\lambda}\)

∴ ν₂ = \(\frac{3.0\times 10^8\,m\,s^{-1}}{750\times 10^{-9}\,m}\)

= 4.00 × 10¹⁴ Hz

The frequency of violet light is 7.50 × 10¹⁴ Hz and that of red light is 4.00 × 10¹⁴ Hz.

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