JEE Advanced 2024 Paper 1, Physics Section 3 Q3: Wave Optics

JEE Advanced2024Paper 1Physics Section 3

A point source $S$ emits unpolarized light uniformly in all directions. At two points $A$ and $B$ , the ratio $r = I_{A} / I_{B}$ of the intensities of light is $2$ . If a set of two polaroids having $4 5^{\circ}$ angle between their pass-axes is placed just before point $B$ , then the new value of $r$ will be _____.

Your answer

Solution

For an isotropic point source, intensity falls as $1/ ℓ^{2}$ . Originally $I_{A} / I_{B} = 2$ .

When unpolarized light passes through a polaroid, the transmitted intensity becomes half. Passing further through a second polaroid whose pass-axis is at $4 5^{\circ}$ multiplies by $cos^{2} 4 5^{\circ} = 1/2$ .

So the intensity reaching $B$ becomes $I_{B}^{'} = \frac{I _{B}}{2} \cdot \frac{1}{2} = \frac{I _{B}}{4}$ .

New ratio: $\frac{I _{A}}{I _{B}^{'}} = \frac{I _{A}}{I _{B} /4} = 4 \cdot \frac{I _{A}}{I _{B}} = 4 \times 2 = 8$ .

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