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Two mirrors an inclined to each other at an angle $\theta$ It produces 5 images for a given object . Then,

$(a)\;30^{\circ} \leq \theta \leq 60^{\circ} \\ (b)\;45 ^{\circ} \leq \theta \leq 60^{\circ} \\ (c)\;60^{\circ} \leq \theta \leq 72^{\circ} \\ (d)\;60^{\circ} \leq \theta \leq 90^{\circ} $

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Since the number of images formed is 5
We have $\large\frac{360}{\theta}$$-1 \leq 5 \leq \large\frac{360}{\theta}$
$\large\frac{360}{\theta} $$-1 \leq 5$
$360 \leq 60$
$\theta \geq 60^{\circ}$
$5 \leq \large\frac{360}{\theta}$
$\theta \leq \large\frac{360}{5}$
$\theta \leq 72^{\circ}$
$\therefore 60^{\circ} \leq \theta \leq 72^{\circ}$
Hence c is the correct answer
answered Jan 17, 2014 by meena.p

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