Question

The angle between the axes of two polarizing filters is \({\rm{45}}{\rm{.}}{{\rm{0}}^{\rm{^\circ }}}\). By how much does the second filter reduce the intensity of the light coming through the first?

Short answer

The second filter reduces the intensity of light by half of the light coming from the first filter.

Step-by-step solution

Definition of Concept 

Intensity: The power transferred per unit area is the intensity of radiant energy in physics, where the area is measured on a plane perpendicular to the energy's propagation direction.

Find how much the second filter reduces the intensity of the light coming through the first

Considering the given information,

Angle between two filters, \(\theta = {45^\circ }\)

Apply the formula,

The intensity of the transmitted wave is proportional to the intensity of the incident wave,

\(I = {I_o}{\cos ^2}\theta \)

Here,

The intensity of transmitted light is denoted by I.

The incident wave's intensity is denoted by\({{\rm{I}}_{\rm{o}}}\).

The angle between the direction of polarised light and the axis of the polarising filter is denoted by the symbol\({\rm{\theta }}\).

Assume the incident wave from the first polarizer filter has an intensity of\({{\rm{I}}_{\rm{o}}}\).

The incident wave's intensity is proportional to the transmitted wave's intensity.

\(I = {I_o}{\cos ^2}\theta \).

Putting the values,

\(\begin{aligned}I &= {I_o}{\cos ^2}45\\I &= \dfrac{{{I_o}}}{2}\end{aligned}\)

Therefore, the second filter reduces the intensity of light by half of the light coming from the first filter.