Question

The frequency of a light wave in air is 4.6 × 10¹⁴ Hz. What is the wavelength of this wave after it enters a pool of water?

300 nm  
490 nm  
650 nm  
870 nm

Answer 1

490 nm

Step-by-step explanation:

Wave length: This is the distance of a complete cycle covered by a wave.

The expression for frequency, wave length and speed is given as,

c = λf.................. Equation 1

Where c = speed of light in water, λ = wave length of light, f = frequency of light.

Also,

n = v/c............. Equation 2

Where n = refractive index of water, v = speed of sound in air.

Making c the subject of the equation,

c = v/n.............. Equation 3

Substitute equation 3 into equation 2

v/n = λf

make λ the subject of the equation

λ = v/nf............... Equation 4

Given: f = 4.6 × 10¹⁴ Hz

Constant: n = 1.33, v = 3.0×10⁸ m/s.

Substitute into equation 4

λ = 3.0×10⁸ /(1.33×4.6 × 10¹⁴ )

λ = 0.49×10⁻⁶ m

λ = 490 nm.

Hence the right option is 490 nm