How Do Different Mirror Combinations Affect Image Formation?
The combination of mirrors refers to the arrangement of two or more mirrors in relation to one another to study their collective effect on image formation. This concept is fundamental in geometrical optics and is frequently assessed in competitive examinations such as JEE Main and Advanced.
Types of Mirror Combinations
Combinations can involve plane mirrors, spherical mirrors (concave and convex), or a mixture of both. Each arrangement results in characteristic patterns of image formation, effective focal length, and specific rules for the number and orientation of images.
Number of Images Formed by Two Plane Mirrors
When two plane mirrors are inclined at an angle θ to each other, an object placed between them produces multiple images due to successive reflections. The number of images (N) depends on the value of θ.
| Mirror Setup | Formula for Image Number |
|---|---|
| Two plane mirrors at angle θ | N = (360°/θ) – 1 (if 360°/θ is integer); else N = integer part of (360°/θ) |
| Two plane mirrors parallel | Infinite images |
If the angle divides 360° exactly, all images formed are distinct. If not, some images overlap or coincide, and N is the integer part of (360°/θ). For parallel mirrors (θ = 0°), the process ideally continues indefinitely, forming infinite images.
This produces complex image arrangements commonly observed in optical devices and can be further studied in the context of Reflection And Transmission Of Waves.
Combination of Spherical Mirrors: Effective Focal Length
When two spherical mirrors are placed in contact with a common principal axis, their combination acts as a single mirror with an effective focal length. The combined effect is obtained using reciprocal addition similar to that used for lenses.
| Setup | Effective Focal Length Formula |
|---|---|
| Two spherical mirrors in contact | $\dfrac{1}{f} = \dfrac{1}{f_1} + \dfrac{1}{f_2}$ |
In the above formula, $f_1$ and $f_2$ are the focal lengths of the individual mirrors, with sign convention: concave mirror ($f > 0$), convex mirror ($f < 0$). Proper sign assignment is essential for accurate calculation.
For compound systems involving both mirrors and lenses, refer to the rules discussed in Combination Of Thin Lenses.
Mirror Formula Application to Series Arrangements
If mirrors are arranged in series (not in contact), the image formed by one mirror acts as the object for the next. The standard mirror formula applies individually at each step: $\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$, where $u$ and $v$ are the object and image distances for each mirror.
Sign conventions for distances and focal lengths must follow rules outlined in Sign Convention Of Lens And Mirror.
Numerical Examples on Combination of Mirrors
Example 1: Two plane mirrors are placed at a 60° angle. To find the number of images: $N = \dfrac{360°}{60°} - 1 = 6 - 1 = 5$ images.
Example 2: For two spherical mirrors in contact, with $f_1 = +20\,\text{cm}$ (concave) and $f_2 = -30\,\text{cm}$ (convex): $\dfrac{1}{f} = \dfrac{1}{20} + \left(-\dfrac{1}{30}\right) = \dfrac{3 - 2}{60} = \dfrac{1}{60}$, so $f = +60\,\text{cm}$. The combination behaves as a concave mirror with a focal length of 60 cm.
Proper handling of these mirror combinations is essential for precise analysis, as explained further in Mirror Formula And Magnification.
Common Errors in Mirror Combination Problems
- Incorrect sign assignment for mirror types
- Confusion when angle does not divide 360°
- Neglecting overlapping or coincident images
- Ignoring image orientation or inversion
- Misapplication of mirror formula for series setups
To avoid mistakes, always ensure the correct application of sign conventions and account for symmetry or overlap in complex image formations. Detailed information about the distinction between lenses and mirrors is available at Difference Between Mirror And Lens.
Applications and Relevance of Mirror Combinations
Combinations of mirrors are frequently used in scientific optical devices, including kaleidoscopes, periscopes, solar concentrators, and certain types of telescopes. Understanding these systems enhances comprehension of practical optics and exam problem-solving.
The use of mirror systems in daily life and advanced experiments demonstrates their significance, further detailed in Uses Of Spherical Mirrors.
FAQs on Understanding the Combination of Mirrors in Physics
1. What is a combination of mirrors?
A combination of mirrors refers to the arrangement of two or more mirrors in specific orientations to study the behaviour of light, such as reflection, image formation, and related phenomena.
- Often used in experiments to explore the laws of reflection
- Common combinations include parallel mirrors, perpendicular mirrors, and inclined mirrors
- Lead to formation of multiple images and special optical effects
2. How many images are formed when two mirrors are placed at right angles?
When two mirrors are placed at right angles (90°), three images of an object are formed.
- This result follows the formula: Images = (360°/θ) - 1, where θ is the angle between the mirrors
- For θ = 90°: Images = (360/90) - 1 = 4 - 1 = 3 images
- This is a common exam question for optics chapters in science syllabus
3. What is the formula for the number of images formed by two mirrors?
The formula for the number of images formed by two mirrors at an angle (θ) is:
- Number of Images (n) = (360°/θ) - 1
- If (360/θ) is odd, then the image count is n
- If (360/θ) is even, one image will coincide, and the formula becomes n - 1
- This concept is highly relevant for CBSE Science exams
4. What happens when two mirrors are placed parallel to each other?
When two mirrors are placed parallel, an infinite number of images are formed.
- Each mirror keeps reflecting the images formed by the other
- This setup is commonly demonstrated in science labs using plane mirrors
- The brightness of images decreases with distance due to partial absorption of light
5. Explain the significance of multiple reflections with mirror combinations.
Multiple reflections with a combination of mirrors allow for the creation of several images and are important for studying the principles of light.
- Help understand laws of reflection and symmetry of image formation
- Used in periscopes, kaleidoscopes, and optical instruments
- Demonstrate how changing the angle affects the number of images
6. What is a kaleidoscope and how does it use the combination of mirrors?
A kaleidoscope is an optical instrument that uses a combination of plane mirrors set at angles, creating multiple symmetrical patterns through reflection.
- Typically constructed using three long, narrow strips of mirrors placed at 60° to each other
- Pieces of colored glass are placed at one end
- Looking into the tube produces beautiful, repeated patterns thanks to multiple reflections
7. How does changing the angle between mirrors affect the number of images formed?
Changing the angle between mirrors directly changes the number of images formed.
- Smaller angles between mirrors lead to a higher number of images
- For 90° angle, 3 images; for 60°, 5 images, and so on
- At 0° (parallel mirrors), infinite images are formed
8. Why do images become fainter in multiple reflections?
Images become fainter with each multiple reflection because some light is absorbed or scattered at every bounce off a mirror.
- Each reflection slightly reduces the intensity of light
- After many reflections, the images appear dim and less distinct
- This happens in both glass and metallic mirrors
9. State the laws of reflection as applied in a combination of mirrors.
Combination of mirrors follows the same laws of reflection:
- The angle of incidence equals the angle of reflection
- Incident ray, reflected ray, and normal all lie in the same plane
- These laws apply at every mirror surface in a combination setup
10. Give three applications of using a combination of mirrors in daily life.
Combinations of mirrors have many daily applications:
- Periscope: Used in submarines and tanks, relies on two mirrors set at 45° angles
- Kaleidoscope: Creates beautiful patterns with multiple mirrors
- Dressing rooms and shops: Use parallel mirrors for multiple angles and images
11. What happens to image formation when the angle between two mirrors is 60 degrees?
When two mirrors are at 60°, five images are formed of a placed object.
- Formula: (360°/60°) - 1 = 6 - 1 = 5 images
- This is a classic textbook question in light reflection chapters
12. Are the images formed by a combination of mirrors real or virtual?
The images formed by a combination of plane mirrors are always virtual and erect.
- Virtual images cannot be obtained on a screen
- They appear to be located behind the mirror(s)
