An electromagnetic wave of frequency 5.0 x 1014Hz, is incident on the surface of water...

WAEC 1998

An electromagnetic wave of frequency 5.0 x 10¹⁴Hz, is incident on the surface of water of refractive index \(\frac{4}{3}\). Taking the speed of the wave in air as 3.0 x 10⁸ms^-1, calculate the wavelength of the wave in water.

A. 2.2 x 10^-6m
B. 1.7 x 10^-7m
C. 8.0 x 10^-7m
D. 6.0 x 10^-7m
E. 4.5 x 10^-7m

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Correct Answer: Option E

Explanation

\(_an_w = \frac{\lambda_a}{\lambda_w}\)

\(\frac{4}{3} = \frac{\lambda_a}{\lambda}\)

\(\lambda_w = \frac{v}{f}\)

= \(\frac{3.0 \times 10^8}{5.0 \times 10^{14}} = 0.6 \times 10^{-6}\)

\(\lambda_w = \frac{3}{4} \lambda_a = \frac{3}{4} \times 0.6 \times 10^{-6}\)

= 4.5 x 10^-7m

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