The total number of images formed by two mirrors inclined at 120° asymmetrically to each other is ______.
3
Calculating Images Formed by Inclined Plane Mirrors
When two plane mirrors are inclined at an angle to each other, multiple images of an object placed between them are formed due to successive reflections. The total number of images formed depends on the angle between the mirrors and the position of the object (symmetric or asymmetric).
Angle Between Mirrors and Object Placement
In this specific problem, the angle between the two mirrors is given as $\theta = 120^\circ$. The object is placed asymmetrically between the mirrors. We need to determine the total number of images formed under these conditions.
Formula for Number of Images
The formula used to calculate the number of images ($n$) formed by two plane mirrors inclined at an angle $\theta$ depends on the value of $\frac{360^\circ}{\theta}$. Let $m = \frac{360^\circ}{\theta}$.
- If $m$ is an even integer, the number of images is $n = m - 1$, irrespective of whether the object is placed symmetrically or asymmetrically.
- If $m$ is an odd integer:
- For symmetric placement of the object, the number of images is $n = m - 1$.
- For asymmetric placement of the object, the number of images is $n = m$.
- If $m$ is not an integer, the number of images is $n = \text{integer part of } m$.
Applying the Formula for 120 Degrees Asymmetrically
First, let's calculate the value of $m = \frac{360^\circ}{\theta}$ for the given angle $\theta = 120^\circ$:
\begin{equation*} m = \frac{360^\circ}{120^\circ} = 3 \end{equation*}
The value $m=3$ is an odd integer. According to the rules mentioned above, when $m$ is an odd integer and the object is placed asymmetrically, the number of images formed is equal to $m$.
Therefore, for $\theta = 120^\circ$ and asymmetric placement, the number of images is $n = m = 3$.
Conclusion on Image Formation
Based on the angle of inclination being 120 degrees, the calculation of $360^\circ/\theta$ gives an odd integer (3). Since the object is placed asymmetrically, the total number of images formed is equal to this odd integer value.
The total number of images formed by two mirrors inclined at 120° asymmetrically is 3.
| Angle ($\theta$) | Value of $m = \frac{360^\circ}{\theta}$ | Type of $m$ | Object Placement | Number of Images ($n$) |
|---|---|---|---|---|
| $120^\circ$ | 3 | Odd Integer | Asymmetric | $m = 3$ |
Revision Table: Images by Inclined Mirrors
| $m = \frac{360^\circ}{\theta}$ | Object Placement | Number of Images ($n$) |
|---|---|---|
| Even Integer | Symmetric or Asymmetric | $m - 1$ |
| Odd Integer | Symmetric | $m - 1$ |
| Odd Integer | Asymmetric | $m$ |
| Not an Integer | Symmetric or Asymmetric | Integer part of $m$ |
Additional Information on Multiple Reflections
The formation of multiple images in inclined mirrors occurs because light rays from the object reflect off one mirror, and these reflected rays then act as virtual objects for the other mirror, leading to further reflections and image formation. The number of images is limited by the angle between the mirrors because subsequent reflections create images that eventually lie outside the angular region between the mirrors, and thus light from those virtual images cannot reach the observer after reflection from both mirrors.
Important Questions from Mirrors and Images
Which one of the following telescopes contains only mirrors?
The correct relation between the radius of curvature R and focal length f of a spherical mirror is
Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when
The image of an object formed by a plane mirror is
The image we see in plane mirror is
