Question

monochromatic light of wavelength 600 NM is incident from air on water .what is the wavelength frequency and speed of refracTed light ​

Answer 1

Explanation:

Wavelength of incident monochromatic light,

λ = 589 nm = 589 × 10−9 m

Speed of light in air, c = 3 × 108 m/s

Refractive index of water, μ = 1.33

(a) The ray will reflect back in the same medium as that of incident ray. Hence, the wavelength, speed, and frequency of the reflected ray will be the same as that of the incident ray.

Frequency of light is given by the relation,

v = c / λ

= 3 x 108 / 589 x 10-9

= 5 .09 x 1014 Hz

Hence, the speed, frequency, and wavelength of the reflected light are 3 × 108 m/s, 5.09 ×1014 Hz, and 589 nm respectively

(b) Frequency of light does not depend on the property of the medium in which it is travelling. Hence, the frequency of the refracted ray in water will be equal to the frequency of the incident or reflected light in air.

So Refracted frequency, ν = 5.09 ×1014 Hz

Speed of light in water is related to the refractive index of water as:

v = c / μ

v = 3 x 108 / 1.33 = 2.26 x 108 m/s

Wavelength of light in water is given by the relation,

λ = v / v

v = 2.26 x 108 / 5 .09 x 1014 = 444.007 x 10-9 m

= 444.01 nm

Hence, the speed, frequency, and wavelength of refracted light are 2.26 ×108 m/s, 444.01nm, and 5.09 × 1014 Hz respectively.

Answer 2

The frequency of refracted light is $5$×$10^{14} Hz$, the speed of refracted light is $2.25$×$10^{8}$ and the wavelength of refracted light is $450nm$.

Step by step explanation

Given data:

Wavelength of monochromatic light$=600nm$

To find:

We must find the speed of refracted light, frequency and the wavelength.

Formula to be used:

• ν$=c/$λ

where: ν$=$frequency of refracted light

$c=3$×$10^{8}$(speed of light)

λ$=$600 nm(wavelength of incident light)

• $v=c/$μ

where: $v=$speed of the refracted light

μ$=$$1.33$ (refractive index of water to air )

• λ'$=v/$ν

Where λ'$=$wavelength of refracted light

Solution:

• using the formula ν$=c/$λ we can calculate the frequency of refracted light

ν$=3$×$10^{8} /600$×$10^{-9}$

$=5$×$10^{14}$$Hz$

• Using the formula$v=c/$μ we can calculate the speed of the refracted light.

$v=3$×$10^{8} /1.33$

$=2.25$×$10^{8}$ $m/s$

• Using the formula λ'$=v/$ν we can determine the wavelength of refracted light.

λ'$=2.25$×$10^{8} /5$×$10^{14}$

$=4.5$×$10^{-7}$

$=450nm$

Therefore the frequency of refracted light is $5$×$10^{14}Hz$, speed is $2.23$×$10^{8} m/s$ and the wavelength is $450 nm$

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