Question

If two plane mirrors are inclined at an angle of 120° to each other, if a point object is placed off the angle bisector between those mirrors, find the number of images obtained​

Answer 1

12th/Physics

Ray optics

Answer :

Angle between two plane mirrors = 120°

A point object is placed off the angle bisector between those mirrors.

We have to find the number of images obtained by plane mirrors$.$

Concept :

When two plane mirrors are inclined at an angle θ and an object is placed between them, the number of images of an object are formed due to multiple reflections.

• n = 360°/θ

★ If n is even number ;

Number of images = (n - 1)

★ If n is odd number ;

Number of images = (n - 1) or n

• (n - 1) if position of object is symmetric
• n if position of object is asymmetric

➙ n = 360°/120° = 3 (odd)

Here, position of object is symmetric.

➙ No. of images = (3 - 1) = 2

Cheers!

Answer 2

Working out:

In the above question, we are given with two mirrors which are inclined at an angle of 120°. And an object is placed on the angle bisector (Symmetrical).

We have to find the number of images formed.

For solving this, we need to know the number of images formed in different cases of two inclined mirrors at an angle of θ.

• If 360° / θ = even number

Then, number of images is (360° / θ)- 1

• If 360° / θ = odd number and placed at angle bisector

Then, number of images is (360° / θ)- 1

• If 360° / θ = odd number and is not placed at angle bisector

Then, number of images is (360° / θ)

• If 360° / θ is not equals to 0,

Then total number of images is the integer number.

So, let's find which case is satisfied by these mirrors,

⇛ 360° / θ = 360° / 120°

⇛ 360° / θ = 3 (odd)

This is odd and placed at angle bisector, So:

⇛ Number of images = 360° / θ - 1

⇛ Number of images = 3 - 1 = 2

Total number of images formed:

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And we are done !!

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