A light ray travelling parallel to the principle axis of a concave mirror strikes the minor at angle of incidence $θ$ . If the radius of curvature of the mirror is $R$ , then after reflection, the ray meets the principle axis at distance $d$ from the centre of curvature, then $d$ is

\frac{R}{2}

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R (1 - \frac{1}{2 cos θ})

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\frac{R}{2 cos θ}

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\frac{R}{2} (1 + cos θ)

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Solution

The correct option is C $\frac{R}{2}$
$\begin{matrix} So in △ A B C \Rightarrow \frac{d}{sin θ} = \frac{R}{sin (π - 2 θ)} [By (sin rule)] \Rightarrow \frac{d}{sin θ} = \frac{R}{sin (2 θ)} \Rightarrow \frac{d}{sin θ} = \frac{R}{2 sin θ cos θ} cos sin 2 θ = 2 sin θ cos θ) \end{matrix}$
$d = \frac{R}{2 cos θ} \Rightarrow$ now as $Q \to 0$
$∴ d = \frac{R}{2}$
Hence obtion 'A is correct.

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