Experiments show that the ground spider uses one of its several pairs of eyes as a polarization detector. In fact, the two eyes in this pair have polarization directions that are at right angles to one another. Suppose linearly polarized light with an intensity of 845 W/m2 shines from the sky onto the spider, and that the intensity transmitted by one of the polarizing eyes is 263 W/m2. For this eye, what is the angle between the polarization direction of the eye and the polarization direction of the incident light

The angle between the polarization direction of the eye and the polarization direction of the incident light = 56.1°

Explanation:

For polarization, the relationship between the intensity of transmitted rays (I), intensity of incident rays (I₀) and the angle between the polarization direction of the eye and the polarization direction of the incident light (θ) is given as

I = I₀ cos²θ

I = intensity of transmitted rays = 263 W/m²

I₀ = intensity of incident rays = 845 W/m²

θ = ?

263 = 845 cos²θ

cos²θ = (263/845) = 0.3112

Cos θ = √0.3112 = 0.5579

θ = cos⁻¹ (0.5579)

θ = 56.1°

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