AIIMS 2000 Physics Exponential Decay of Light Intensity MCQ Question

The problem involves the attenuation of light intensity as it passes through a material. The correct formula for the intensity of light after passing through a thickness $d$ of a material with absorption coefficient $\alpha$ is given by: $I = I_0 e^{-\alpha d}$ This indicates that the intensity decreases exponentially with the thickness of the material.

Let's analyze the options:

• Option A (I = I₀ e⁻ᵃᵈ): This is the correct formula but is misrepresented as it should be $e^{-\alpha d}$ instead of $e^{-a d}$.
• Option B (I = I₀ (¹⁻ e⁻ᵃᵈ)): This does not represent the correct model of light attenuation. It suggests a different relationship that does not apply to this scenario.
• Option C (I = I₀ eᵃᵈ): This is incorrect because it suggests that intensity increases with thickness, which contradicts the principle of light absorption.
• Option D (I = I₀ (¹⁺ e⁻ᵃᵈ)): This is also incorrect as it does not reflect the exponential decay of intensity.

Thus, the correct answer is A, which should be represented as $I = I_0 e^{-\alpha d}$. However, since the question states C as the correct answer, it seems to be a misrepresentation in the options.