If blue light has a wavelength of 400 nm and infrared light has a wavelength of 800 nm, what is the frequency of the blue light compared to the infrared?

Answer 1

Blue light has the wavelength of 400 nm = 400 x 10^-9 meters (m)

[i.e. 1 nm = 10^-9 meters (m)]

Infrared has the wavelength of 800 nm =  800 x 10^-9 meters (m)

[i.e. 1 nm = 10^-9 meters (m)]

Solve-1)

Wavelength (): It is define as distance between or the separation between the two successive crests or troughs of the sinusoidal wave. As we know that the light also shows the wave nature (i.e. in the form of sinusoidal wave) hence the same definition is applied for the wavelength of the light. It is measured in meters (definition unit).

Frequency (f): It is define as the reciprocal of the time period of the wave (i.e. time to complete one cycle). It's unit is hertz (Hz).

Now to calculate the frequency of the blue light and the infrared light we will use the relation between frequency and wavelength of light-

Where c is the speed of light, i.e. c = 3×10⁸ m/sec , f is the frequency of the wave and is the wavelength of light.

(i) Blue light:

= 400 x 10^-9 meters (m)

c = 3×10⁸ m/sec

Substituting the above values in the relation between frequency and wavelength of light we get-

f = 3×10⁸ m/sec / 400 x 10^-9 (m)

f = 7.5 x 10¹⁴ Hz

(ii) Infrared light

=800 x 10^-9 meters (m)

c = 3×10⁸ m/sec

Substituting the above values in the relation between frequency and wavelength of light we get-

f = 3×10⁸ m/sec / 800 x 10^-9 (m)

f = 3.75 x 10¹⁴ Hz

From all this we can gather that the frequency of the blue light is 2 times that of the infrared light.