A certain laser emits light in a narrow band of wavelengths centered at 517.5 nm

Question

A certain laser emits light in a narrow band of wavelengths centered at 517.5 nm and with a ''wavelength width'' (such as on the scale of the figure) of 0.00857 nm. What is the corresponding ''frequency width'' for the emission in Hz?

Wavelength (nm) 700 600 500 400 --. Visible spectrum wavelength (m) s s 10-2 |(310-41(p5 10d. 108 107 10° 105 104 10° 102 10 I 10" IT' 10-810"910-1°10-11 1(ri2 10-1310"1410-15 lpli Long waves Radio waves Infrared UltravioletX ravs Gamma rays 10 02 103 101 105 112 1013 104 1015 1016 1017 1018 12 10010212 Frequency (Hz) FM radio IV channels Maritime and aeronauical uses AM radio Maritime aeronautical and mobile radio Marite, aeronautical, citizens band and mobile radio 1010 Frequency (Hz)

Explanation / Answer

lamda1 = 517.5 - 0.00857/2 nm

= 517.495715 nm

lamda2 = 517.5 + 0.00857/2 nm

= 517.504285 nm

we know, f = c/lamda

so,

f1 = c/lamda1 = 3*10^8/(517.495715*10^-9)

= 5.797149*10^14 hz

f2 = c/lamda2 = 3*10^8/(517.504285*10^-9)

= 5.797053*10^14 hz

so, frequency width = f1 - f2

= 5.797149*10^14 - 5.797053*10^14

= 9.6*10^10 hz

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