Final answer:
In physics, when polarizing filters are applied to light, the intensity is reduced based on the angle of the polarizer's axis. To achieve 10% transmittance through a third polarizer, the angle must be around 71.6 degrees, calculated using Malus's Law and known intensity reduction at specific angles.
Step-by-step explanation:
The question revolves around the concept of light polarization and the use of polarizing filters to alter the intensity of light that passes through them. This topic is grounded in the field of physics, more specifically within the study of waves and optics.
When dealing with multiple polarizing filters, the intensity I of transmitted light can be determined using Malus's Law, which states that I is proportional to the cosine squared of the angle θ between the light's polarization direction and the axis of the polarizer:
I = I0cos2(θ),
where I0 is the initial intensity of light before passing through the polarizer. To achieve a total transmittance of 10% of the incident light, we need to find the angle θ that satisfies the following condition:
Ifinal = 0.10I0.
Using Malus's Law and considered that the light intensity is halved (reduced to 50%) after passing through a polarizer at a 45° angle, a bit of trigonometry leads us to conclude that a polarization axis of 71.6° for the third polarizer would bring the intensity down to nearly 0%. Thus, to achieve 10% transmittance, an angle slightly less than 71.6° but greater than 45° is needed, symmetrical to the angle that gives 90% transmittance, which is 18.4°.
Through this understanding and application of Malus's Law, trigonometric identities, and the given information about polarization percentages at certain angles, we arrive at our conclusion. For a final intensity to be 10%, the third polarizer should have its axis at an angle of approximately 71.6° with respect to the vertical.
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