Question

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For a given light of wavelength 600 nm , wavelength width is 0.2 nm . Find frequency width ?

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Answer 1

$\text{Wavelength of light}( \lambda )= 600 \: nm$

$\text{Wavelength width}( \delta \lambda )= 0.2 \: nm$

$\text{Wavelength range} = \lambda \pm \delta \lambda = 600 \: nm \pm 0.2nm$
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$\lambda_{lower} = (600 - 0.2)nm = 599.8nm = 5.998 \times {10}^{ - 7} m$

$\lambda_{upper} = (600 + 0.2)nm = 600.2nm = 6.002 \times {10}^{ - 7} m$

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$f_{upper} = \frac{c}{\lambda_{lower}} = \frac{3 \times {10}^{8} }{5.998 \times {10}^{ - 7} } = 5.001667 \times {10}^{14} \: hz$

$f_{lower} = \frac{c}{\lambda_{upper}} = \frac{3 \times {10}^{8} }{6.002 \times {10}^{ - 7} } = 4.998334\times {10}^{14} \: hz$

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$\text{Range of frequency} = f_{upper} - f_{lower} \\ \\ = 5.001667 \times {10}^{14} - 4.998334 \times {10}^{14} \\ \\ =0 .003333 \times {10}^{14} \\ \\ = 3.333 \times {10}^{11} hz$

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$\text{frequency width} = \frac{range}{2} \\ \\ = \frac{3.333 \times {10}^{11} }{2} = 1.667 \times {10}^{11} \: hz$


$\boxed{ \large\red{ \text{ frequency width} = 1.667 \times {10}^{11} \: hz}}$

Answer 2

Answer:1.67 × 10^11 Hz

Explanation:

∆f = c∆lambda/ lambda^2