Question

A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is, the intensity of the emerging beam is I. If you now want the intensity to be I/2, what should be the angle (in terms of) between the polarizing angle of the filter and the original direction of polarization of the light?

Short answer

the angle between the polarizing angle of the filter and the original direction is

Step-by-step solution

Malus’s law

According to Malus' law, the intensity of plane-polarized light that travels through an analyzer varies as the square of the cosine of the angle between the plane of the polarizer and the analyzer’s transmission axes.

$\mathit{l}\mathbf{\to }$the intensity of polarised light that passes through an analyzer

${\mathit{l}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\to }$maximum transmitted light

$\mathit{\varphi }$angle between the polarization axis of light and the analyzer

Angle between the polarizing angle of filter and original direction

Using malus’s law;

Substituting;

Hence, the angle between the polarizing angle of the filter and the original direction is