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10.1 Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index of water is 1.33.

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Payal Gupta | Contributor-Level 10

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10.1 Wavelength of incident monochromatic light, $?$ = 589 nm = 589 $* 10^{- 9}$ m

Speed of light in air, c = 3 $* 10^{8}$ m/s

Refractive index of water, $?$ = 1.33

In case of reflection, the ray goes back to the same medium. Hence wavelength, frequency and speed of reflected beam will be same as incident beam.

Frequency of light beam is given by the relation, $?$ = $\frac{c}{?}$ = $\frac{3 * 10^{8}}{589 * 10^{- 9}}$ = 5.09 $* 10^{14}$ Hz.

Hence speed = 3 $* 10^{8}$ m/s, Wavelength = 589 $* 10^{- 9}$ m, Frequency = 5.09 $* 10^{14}$ Hz of incident ray and reflected ray will remain unchanged.

(i) Frequency = does not depend on the property of the medium in

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10.1 Wavelength of incident monochromatic light, $?$ = 589 nm = 589 $* 10^{- 9}$ m

Speed of light in air, c = 3 $* 10^{8}$ m/s

Refractive index of water, $?$ = 1.33

In case of reflection, the ray goes back to the same medium. Hence wavelength, frequency and speed of reflected beam will be same as incident beam.

Frequency of light beam is given by the relation, $?$ = $\frac{c}{?}$ = $\frac{3 * 10^{8}}{589 * 10^{- 9}}$ = 5.09 $* 10^{14}$ Hz.

Hence speed = 3 $* 10^{8}$ m/s, Wavelength = 589 $* 10^{- 9}$ m, Frequency = 5.09 $* 10^{14}$ Hz of incident ray and reflected ray will remain unchanged.

(i) Frequency = does not depend on the property of the medium in which it is travelling, hence frequency will remain same, i.e. 5.09 $* 10^{14}$ Hz

(ii) Speed of light in water depends upon the refractive index of water, hence speed of light, v = $\frac{c}{?}$ = $\frac{3 * 10^{8}}{1.33}$ = 0.226 $* 10^{9}$ m/s

Wavelength in water, $?$ = $\frac{v}{?}$ = $\frac{0.226 * 10^{9}}{5.09 * 10^{14}}$ = 4.432 $* 10^{- 7}$ m = 443.2 nm

Hence the speed, frequency and wavelength of refracted light are 0.226 $* 10^{9}$ m/s, 5.09 $* 10^{14}$ Hz and 443.2 nm

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10.1 Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index of water is 1.33.

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