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A plane polarized light is incident normally on a tourmaline plate. Its ⃗E vectors make an angle of 60° with the optic axis of the plate. Find the percentage difference between initial and final intensities.

Asked in GUJCET 2015 · Malus's law and polaroids

• (1) 50%
• (2) 25%
• (3) 75%
• (4) 90%

Step-by-step solution

Why the other options are wrong

• (1) This uses cos 60° = 1/2 without squaring it, so the light getting through is taken as (I₀)/2 and the loss as 50%. At 60° it is the *amplitude* that is halved; intensity goes as the square of the amplitude, so a half becomes a quarter.
• (2) This is the fraction that gets through, cos²60° = 1/4, quoted as if it were the fraction lost. The question asks for the difference between the initial and the final intensity, which is the other three quarters.
• (4) No single slip gives 90%. Sanity check: cos²60° = 0.25, so a quarter of the light is transmitted and 100 - 25 = 75% of it is lost.

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