If two mirrors are kept at 60 degrees to each other, then the number of images formed by them is
(a)

Q: What if the value of $360/\theta$ is odd?

If it's odd, the number of images is $m-1$ if the object is placed symmetrically, and $m$ if placed asymmetrically.

Q: Why do we subtract 1 when $m$ is even?

When $m$ is even, the last images formed by both mirrors overlap and coincide, so we count them as one instead of two.

Q: Are all images formed on a circle?

Yes, all images and the object lie on a circle whose center is the intersection point of the two mirrors.

Q: What if the mirrors are parallel?

If mirrors are parallel, $\theta = 0^\circ$, so $360/0$ tends to infinity. Infinite images are formed.

Q: Does the position of the object matter for $\theta = 60^\circ$?

No, because $360/60 = 6$, which is even. For even values, the number of images is always $m-1 = 5$, regardless of the object's position.

Question

If two mirrors are kept at $60^\circ$ to each other, then the number of images formed by them is

Options:

(A) 5

(B) 6

(C) 7

(D) 8

Sigma Percentile · Accepted Answer

The phenomenon of multiple reflections is one of the most fascinating visual effects in optics. When you place an object between two inclined plane mirrors, the light rays bounce back and forth between the mirrors, creating a cascade of virtual images. But how do we know exactly how many images will be formed? Let's dive into the mathematics behind this optical illusion.

### Analyzing the Setup

Imagine two plane mirrors, $M_1$ and $M_2$, placed such that the angle between them is $	heta = 60^\circ$. An object $O$ is placed somewhere in the space between these two mirrors.

Every time light from the object hits a mirror, it reflects and forms a virtual image. This image can then act as a virtual object for the second mirror, creating another image, and so on. Interestingly, all these images, along with the original object, lie on the circumference of a circle whose center is the point where the two mirrors intersect.

### The Master Equation

To find the total number of images formed, we use a simple yet powerful formula. First, we calculate a ratio $m$, which tells us how many times the angle $	heta$ fits into a full circle ($360^\circ$):

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

Once we have $m$, we look at its value to determine the number of images $n$:
- If $m$ is an **even integer**, the number of images is always $n = m - 1$, regardless of where the object is placed between the mirrors.
- If $m$ is an **odd integer**, the number of images depends on the object's position. If it's placed exactly on the angle bisector (symmetrically), $n = m - 1$. If it's placed asymmetrically, $n = m$.

### Final Calculation

Let's apply this to our specific problem where $	heta = 60^\circ$.

Substituting the value into our formula:

$$m = \frac{360^\circ}{60^\circ} = 6$$

We get $m = 6$, which is an **even number**. According to our rules, when $m$ is even, we must subtract 1 to find the total number of distinct images. Why do we subtract 1? Because the final images formed by both mirrors overlap perfectly at the same position, so we only count them as a single image.

$$n = 6 - 1 = 5$$

**Thus, exactly 5 images are formed.**

Next time you visit a mirror maze or see two mirrors angled towards each other, you'll know exactly how to predict the number of reflections you'll see!

Animated Solution for Physics - Optics: If two mirrors are kept at $6 0^{\circ}$ to each other, then the number of images formed by them is

Select Answer:

Visualized Solution

$Angle Between Mirrors$

$Formula for Number of Images$

$Calculating m$

$Evaluating m$

$Total Number of Images$

$What if the angle changes?$

The Sigma Insight: Plane Mirror

Analyzing the Setup

The Master Equation

Final Calculation

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Animated Solution for Physics - Optics: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If two mirrors are kept at 60∘ to each other, then the number of images formed by them is