The image of an object O due to reflection fr | vedclass

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(C) The ripples act as plane mirrors reflecting light to form an image with an angular extent $\delta$.Given that $O$ and $E$ are at the same height,$

Vedclass · Accepted Answer

$2 \alpha$

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(C) The ripples act as plane mirrors reflecting light to form an image with an angular extent $\delta$.Given that $O$ and $E$ are at the same height,$O E B C$ forms a trapezium with $O E \parallel B C$.Let $\beta$ be the angle of incidence at point $B$ and $\gamma$ be the angle of incidence at point $C$.From the geometry of the reflection,the angle of the reflected ray with the horizontal is affected by the tilt $\alpha$ of the mirror surface.Using the law of reflection and the geometric properties of the angles shown in the diagram:$\angle 1 = 90^{\circ} - \beta - \alpha$$\angle 2 = 90^{\circ} - \gamma - \alpha$Since $O$ and $E$ are at the same height,the symmetry implies $\beta = \gamma$.The angular extent $\delta$ is the angle subtended by the reflected rays at the observer $E$.From the triangle geometry,the total deviation caused by the tilted mirrors results in $\delta = 2 \alpha$.

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