Q35E - University Physics with Modern Physics

Question

A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of I) of scattered light in the middle of (a) the red part of the spectrum and (b) the violet part of the spectrum. Consult Table 32.1

Step-by-Step Solution

Answer

a) The intensity of scattered light in the middle of the red part of the spectrum is 

b) The intensity of scattered light in the middle of the violet part of the spectrum 

Step 1: Formula

The relation between the intensity of the light and the wavelength of the light;

$l=\frac{c}{{\lambda }_4}$

Here;

I=intensity

$\lambda =$wavelength

c=constant

Step 2: Average wavelength

The average wavelength for green, red, and violet;

Step 3: Intensity of scattered light in the middle of the red part of the spectrum

(a) Assuming $l_G$ and $l_R$ are the intensities of green and red light and ${\lambda }_G$ and ${\lambda }_R$ are the wavelengths of green and red light.

Hence, the intensity of scattered light in the middle of the red part of the spectrum is $l_V=0.3651l$

Step 4: Intensity of scattered light in the middle of the violet part of the spectrum

(b) Assuming $l_G$ and $l_V$ are the intensities of green and violet light and ${\lambda }_G$ and ${\lambda }_v$ are the wavelengths of green and violet light.

Hence, the intensity of scattered light in the middle of the violet part of the spectrum is