Unpolarizedlight of intensity i_0 is incident on three polarizingfilters. the axis of the first is vertical, that of the secondis 60.0 ^\circ from vertical, andthat of the third is horizontal.

what light intensityemerges from the third filter? (i0)

To solve this problem it is necessary to apply the concepts related to the law of Malus which describe the intensity of light passing through a polarizer. Mathematically this law can be described as:

Where,

Indicates the intensity of the light before passing through the polarizer

I = Resulting intensity

= Indicates the angle between the axis of the analyzer and the polarization axis of the incident light

From the law of Malus when the light passes at a vertical angle through the first polarizer its intensity is reduced by half therefore

In the case of the second polarizer the angle is directly 60 degrees therefore

In the case of the third polarizer, the angle is reflected on the perpendicular, therefore, its angle of index would be

Then,

Then the intensity at the end of the polarized lenses will be equivalent to 0.09375 of the initial intensity.

it is the second option.