 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s19/3/a/solution

Use the explicit equation

n / n_{c} = 0.002

; the surrounding phrase reverses the verbal ratio. It gives

n_{c} = 2.0 \times 1 0^{21}

^{- 3}

. From

ω_{0}^{2} = n_{c} e^{2} / (ϵ_{0} m_{e})

λ = 2 π c ϵ_{0} m_{e} / (n_{c} e^{2}) ≃ 0.747 μ m .

This is an underdense optical plasma. Treating the ratio as

n_{c} / n = 0.002

would instead contradict the specified underdense condition.

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