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Chapter 4: Q63E (page 138)

A 1 fs pulse of laser light would be 0.3μmlong. What is the range of wavelengths in a 0.3Imlong pulse of (approximately)600nmlaser light?

Short Answer

Expert verified

The range of wavelength=95.5nm

Step by step solution

01

Formula of wavelength.

Distance between two corresponding points of two consecutive waves.

E=hcλ

Where

c is the speed of light,

λis the wavelength.

his Planck’s constant.

02

Use the wavelength formula for calculation.

Write it as,

E=hcλ

On derivation,

dE=-hcλ2dλdλ=-λ2hcdE

After ignoring the negative sign, the equation can be rewritten as:

dλ=λ2hcdEdE=h4π∆t

Substitute the given values in the equation

dλ=λ2hch4πΔtdλ=λ2hc14π∆tdλ=600×10-924π×3×108×1×10-15dλ=95.5nm

Hence, the 1fs pulse covers a range of wavelengths equal to this value, you may note also that we have taken the absolute value throughout the derivation, however, the range in general could be positive or negative.

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