Question

Explain the successive reflection when the two plane mirrors inclined at any angle.
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Answer 1

Answer:

Ô=360°-2θ

⇒300°=360°-2θ

⇒θ=30°

∴no of images formed is

n=(360°/θ)-1

⇒n=(360°/30°)-1

⇒n=11

∴ no of images formed =11

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Answer 2

Let, M1 and M2 be the two plane mirrors inclined to each other any angle, say, 60°. With C as the centre and radius equal to CM1 draw a circle. Let O be a point object situated on the circumference of this circle. From O draw perpendicular to CM1 cutting CM, at A and produce it to meet the circumference at I₁CA are congruent.

[∴ OC = CI₁, CA is common, ∠OAC = ∠I₁CA = 90°]

∴ OA = AI₁

Thus, I₁ will bw the image of O after reflection from M₁. Further since,

 ∠OCM₁ = ∠I₁CM₁

∴ arc OM₁ = arc M₁I₁

Thus, the position of the image can be located by locating a point I₁ on the other side of M₁ situated at the equal length of arc.

I₁ is situated in front of a plane mirror M₁. Therefore, its image after reflection through M₂ will be obtained at I₂ such that,

arc M₂I₁ = arc M₂I₂

Now, I₂ is located in front of M₁, it will produce an image I₃ such that,

arc M₁I₂ = arc M₂I₂

Now, I₂ is located in front of M₁, it will produce an image I₃ such that,

arc M₁I₂ = arc M₁I₃

If we consider a beam starting from O and directed towards M₂, a set of images I'₁, I'₂ and I'₃ are produced. It will further, be observed that the image I₃ and I'₃will be co-incident.

Thus, five images are observed, if the object is situated in between two mirrors inclined at 60° with each other.