To get three images of a single object, one should have two plane mirrors at an angle of
(a) 60°
(b)

Q: Why do we subtract 1 in the formula?

We subtract 1 because the last images formed by both mirrors overlap perfectly and form a single image. Without subtracting 1, we would be double-counting that overlapping image.

Q: What if $360/\theta$ is not an integer?

If $360/\theta$ is not an integer, the number of images is generally the integral part of the result, though the exact number can depend on the specific position of the object.

Q: Does the position of the object matter?

Yes! If $360/\theta$ is an odd integer, placing the object symmetrically on the angle bisector gives $m-1$ images, while placing it asymmetrically gives $m$ images.

Q: How are the images arranged in space?

The object and all its images always lie on the circumference of a circle. The center of this circle is the intersection point of the two mirrors.

Q: What happens if the mirrors are parallel?

If the mirrors are parallel, the angle $\theta$ is $0^\circ$. Since $360/0$ approaches infinity, an infinite number of images are formed, like when you stand between two mirrors in a dressing room.

Question

To get three images of a single object, one should have two plane mirrors at an angle of

Options:

(A) $60^\circ$

(B) $90^\circ$

(C) $120^\circ$

(D) $30^\circ$

Sigma Percentile · Accepted Answer

### The Magic of Multiple Reflections

Imagine standing in a room where two large mirrors meet at a corner. When you look into them, you don't just see one reflection of yourself; you see a crowd! This fascinating phenomenon occurs because of **multiple reflections**. The image formed by the first mirror acts as a virtual object for the second mirror, which then creates another image, and this process continues until the light rays can no longer reflect between the mirrors.

But how do we know exactly how many images will be formed? Physics gives us a beautifully simple mathematical tool to predict this.

### The Master Equation

The number of images, denoted by $n$, formed by two plane mirrors inclined at an angle $	heta$ is given by a standard formula. When the object is placed symmetrically, or when $\frac{360^\circ}{	heta}$ is an even integer, the formula is:

$$n = \frac{360^\circ}{	heta} - 1$$

You might wonder, why do we subtract $1$? The subtraction accounts for the fact that the final images formed by both mirrors perfectly overlap each other, merging into a single image. If we didn't subtract $1$, we would be double-counting that final overlapping image!

### Solving the Mystery

In our specific problem, we are given the final outcome: exactly $3$ images are formed. Our mission is to work backward and find the angle $	heta$ between the mirrors.

Let's substitute the known value into our master equation:

$$3 = \frac{360^\circ}{	heta} - 1$$

Now, we just need to perform some basic algebra. Let's move the $-1$ to the left side of the equation:

$$3 + 1 = \frac{360^\circ}{	heta}$$

$$4 = \frac{360^\circ}{	heta}$$

Rearranging the equation to solve for $	heta$, we get:

$$	heta = \frac{360^\circ}{4}$$

### The Final Revelation

Dividing $360^\circ$ by $4$ gives us our final answer:

$$	heta = 90^\circ$$

This means that to get exactly three images of a single object, the two plane mirrors must be placed exactly perpendicular to each other, forming a right angle.

**Bonus Geometric Insight:** Did you know that the object and all of its images always lie on the circumference of a perfect circle? The center of this circle is exactly at the point where the two mirrors intersect, and its radius is the distance from the intersection to the object. Physics is not just about equations; it's about the hidden geometry of the universe!

Animated Solution for Physics - Optics: To get three images of a single object, one should have two plane mirrors at an angle of

Select Answer:

Visualized Solution

$Number of Images$

$Formula for Number of Images$

$Substituting the Values$

$Solving for θ$

$Final Answer$

$What if \frac{36 0 ^{\circ}}{θ} is odd?$

The Sigma Insight: Plane Mirror

The Magic of Multiple Reflections

The Master Equation

Solving the Mystery

The Final Revelation

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Animated Solution for Physics - Optics: To get three images of a single object, one should have two plane mirrors at an angle of

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Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Number of Images

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Formula for Number of Images

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Substituting the Values

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Solving for θ

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Final Answer

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } What if θ360∘​ is odd?