A light beam of diameter D is incident on a concave mirror with radius of curvature R as shown in figure. Radius of opaque disc in cm that should be placed at a distance of R/2 from pole such that we don't get reflected light beyond disc is. [Given R=D=10cm]

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Solution

$C D = D P = \frac{R}{2} & A C = R$

DB=CB-CD where $c o s θ = \frac{R}{2 C B}$

$D B = \frac{R}{2 c o s θ} - \frac{R}{2}$

$t a n 2 θ = \frac{r}{D B} \Rightarrow r = D B t a n 2 θ$

$s i n θ = \frac{D}{2 R} = \frac{1}{2} \Rightarrow θ = 30^{\circ}$

$∴ r = 1.35 c m$

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A light beam of diameter D is incident on a concave mirror with radius of curvature R as shown in figure. Radius of opaque disc in cm that should be placed at a distance of R/2 from pole such that we don't get reflected light beyond disc is. [Given R=D=10cm]

CD=DP=R2 &AC=R DB=CB-CD where cosθ=R2CB DB=R2cosθ−R2 tan2θ=rDB ⇒ r=DB tan2θ sinθ=D2R=12⇒θ=30∘ ∴r=1.35 cm

$C D = D P = \frac{R}{2} & A C = R$

DB=CB-CD where $c o s θ = \frac{R}{2 C B}$

$D B = \frac{R}{2 c o s θ} - \frac{R}{2}$

$t a n 2 θ = \frac{r}{D B} \Rightarrow r = D B t a n 2 θ$

$s i n θ = \frac{D}{2 R} = \frac{1}{2} \Rightarrow θ = 30^{\circ}$

$∴ r = 1.35 c m$