Two plane mirrors at an angle such that a ray incident on a mirror undergoes a total deviation of $240^{0}$ after two reflections. Then,

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the angle between the mirror is $60^{0}$

the number of images formed by this system will be 5, if an object is placed symmetrically between the mirrors.

the no. of images will be 6 if an object is kept unsymmetrically between the mirrors.

a ray will retrace its path after 2 successive reflections, if the angle of incidence on one mirror is $60^{0}$ .

answer is A, B, C, D.

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Detailed Solution

A) Total deviation due to two reflection
$d = 360 - 2 θ \Rightarrow 240 = 360 - 2 θ \Rightarrow θ = 60^{0}$

B) $\frac{360}{θ} = 6$ . This is even. As the object is placed symmetrically between the mirrors $N = \frac{360}{θ} - 1 = 5$

C) If the object is placed un symmetrically $N = \frac{360}{θ} = \frac{360}{60} = 6$

D) When a ray incidents on $M_{1}$ at $60^{0}$ , it falls on $M_{2}$ normally as shown in figure.
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