A polarizer and an analyzer are oriented so that the maximum amount of light is transmitted. To what fraction of its maximum value is the intensity of the transmitted light reduced when the analyzer is rotated through `(a) 30^@,(b) 45^@ , ( c) 60^@` ?

Explanation

To solve the problem, we will use Malus's Law, which states that when polarized light passes through a polarizer (analyzer), the intensity of the transmitted light is given by:

\[ I = I_0 \cdot \cos^2(\theta) \]

where:
- \( I \) is the transmitted intensity,
- \( I_0 \) is the initial intensity (maximum intensity when the analyzer and polarizer are aligned),
- \( \theta \) is the angle between the light's polarization direction and the axis of the analyzer.
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