How to Calculate Number of Images in a Combination of Plane Mirrors?
Combination of Mirrors is a fundamental concept in JEE Main Physics, where two or more mirrors are used together to create multiple images and unique optical setups. This topic connects core ideas from reflection, image formation, and focal length, helping students solve tricky numerical problems efficiently. Everyday examples include periscopes, dressing mirrors at angles, and certain scientific instruments where image manipulation is crucial.
In a combination of mirrors, image formation depends on the relative positions and types of mirrors involved. By applying the laws of reflection and systematic ray tracing, students can predict both the number and location of images. This is not just an exam topic—its applications are found in laser alignment tools, kaleidoscopes, and car rearview mirror systems.
The behavior of combinations is different for plane mirrors (flat, non-focusing) and spherical mirrors (curved, focusing). Understanding the distinction is key to choosing the right formulas and approaches in physics problems.
Basic Theory Behind Combination of Mirrors
When light reflects off one mirror and then another, each surface follows the law of reflection: the angle of incidence equals the angle of reflection. In a two-mirror system, the final image can appear shifted, inverted, or even multiple times, depending on the angular separation and type of mirrors used.
With plane mirrors, images form behind each surface at equal distances, while spherical mirrors (concave or convex) use focal length and radius of curvature to focus or diverge the light. Ray diagrams are essential to visualize image order and path.
Formulas for Combination of Mirrors
JEE Main students must master two primary formula sets: one for the number of images (multiple reflections) and another for the equivalent focal length of mirrors in contact. Always remember to check the sign convention and the mirror types involved.
| Setup Type | Formula | Key Notes |
|---|---|---|
| Number of images by two plane mirrors at angle θ | N = (360°/θ) – 1 | If 360°/θ is even, else N = (360°/θ) |
| Effective focal length (f) of two spherical mirrors in contact | 1/f = 1/f1 + 1/f2 | f1, f2: focal lengths. Use sign convention! |
| Object distance formula (mirrors in series) | Apply mirror formula successively | 1/f = 1/v + 1/u (per mirror) |
For a combination of spherical mirrors, use the sign conventions from the mirror formula: Positive for concave (real focus, left), negative for convex (virtual focus, right).
The number of images is affected by the angle between two plane mirrors. For θ = 90°, you get 3 images; for θ = 60°, there are 5 images. Superstition aside, if both mirrors are perfectly parallel, an infinite number of images are created.
Numerical Examples and Image Formation in Combination of Mirrors
Problem 1: Two plane mirrors are placed at 60°. How many images will be seen of an object placed between them?
- Given θ = 60°, N = (360°/θ) – 1
- N = (360°/60°) – 1 = 6 – 1 = 5 images
Problem 2: Find the effective focal length (f) if a concave mirror (f1 = +20 cm) and a convex mirror (f2 = –30 cm) are kept in contact.
- 1/f = 1/f1 + 1/f2 = 1/20 + (–1/30)
- 1/f = (3 – 2)/60 = 1/60 ⇒ f = +60 cm
- The equivalent mirror behaves as a concave mirror with 60 cm focal length.
Stepwise ray diagrams help to confirm the position, orientation, and number of images, especially in exam situations. Master image formation rules for concave mirrors for complex setups.
Common Mistakes and Exam Tips for Combination of Mirrors
- Always apply the correct sign convention for mirror types in formulas.
- Count intersection images when object is placed off the angle’s bisector.
- For plane mirrors at θ, round N down if (360°/θ) is not an integer.
- Do not forget the object itself as a possible real/virtual image.
- Use ray diagrams for orientation and inversion checks.
Students should double-check mirror orientation in diagrams, as left-right inversion and image count traps are common in JEE questions. Practicing a few multiple mirror arrangement problems boosts accuracy under time pressure.
Advanced Applications and Mixed Mirror-Lens Systems
In JEE Main Physics, combinations can include lenses and mirrors together, as in telescopes or microscopes. The formula for combination of lenses is similar: 1/F = 1/f1 + 1/f2 + …, using the proper sign. For three or more mirrors, extend pairwise combinations iteratively.
Real-life setups include periscopic vision, optical bench experiments, and the functioning of reflecting telescopes. The kaleidoscope toy and certain scientific devices use multiple angled mirrors for beautiful repeating image effects.
Strong foundation in the combination of mirrors is critical for high-scoring JEE chapters. For revision, see Optics Revision Notes and attempt problems from previous years on Vedantu for exam-like practice.
- Review sign conventions in optics carefully.
- Compare with lens and mirror differences for concept clarity.
- Visualize image formation using plane mirror image velocity techniques.
- Practice with JEE Physics question-answers for similar image arrangement logic.
- Explore more about uses of spherical mirrors in daily life and labs.
Mastering the combination of mirrors bridges conceptual gaps and boosts problem-solving speed—skills essential for every ambitious physics learner on Vedantu.
FAQs on Combination of Mirrors: Concepts, Formulas & Examples
1. What is the formula for the combination of mirrors?
The formula for the combination of mirrors gives the effective focal length when two spherical mirrors are placed coaxially in contact. The combined focal length (f) is calculated as:
1/f = 1/f1 + 1/f2
Key points:
- This equation is similar to the lens combination formula.
- Use f1 and f2 as the focal lengths of each mirror (convex or concave, taking signs accordingly).
- Commonly asked in JEE and Board exams as part of mirror system numericals.
2. How do you calculate the number of images formed by two plane mirrors?
The number of images formed by two plane mirrors at an angle θ is given by:
N = (360°/θ) – 1 (if 360°/θ is an integer)
Else, use N = integer part of (360°/θ).
- If the object is placed symmetrically, all images are possible.
- If θ is a factor of 360°, an extra image forms at symmetrical positions.
- Very common in school and entrance exams for multiple mirror numericals.
3. What is meant by the combination of mirrors in physics?
The combination of mirrors refers to the arrangement of two or more mirrors together to study how they form images.
- This can include plane mirrors, spherical mirrors (concave or convex), or a mix.
- Leads to unique image formations, changes in focal length, and new reflection paths.
- Used in optical instruments, periscopes, solar concentrators, and exam problems.
4. Can two mirrors together make infinite images?
Yes, two mirrors facing each other parallelly will theoretically form infinite images.
- Each image from one mirror acts as an object for the other, creating a repeating pattern.
- This is commonly used to explain the concept of infinite image formation in introductory optics.
- In real life, the number is limited by mirror quality and light absorption.
5. How is the combination of mirrors used in real life?
Combinations of mirrors are used in several real-world applications:
- Periscopes and kaleidoscopes (for image duplication)
- Solar cookers (concentrating sunlight with multiple mirrors)
- Reflecting telescopes (combining concave and plane mirrors)
- Security arrangements (wide angle viewing)
6. Does the formula for combination of mirrors change if one is convex and one is concave?
The basic mirror combination formula stays the same: 1/f = 1/f1 + 1/f2.
- BUT, assign proper plus (+) or minus (–) sign to focal length based on the type: concave (f > 0) and convex (f < 0).
- Correct sign convention is essential for accurate results in spherical mirror combinations.
7. What happens when the angle between two mirrors is not a perfect divisor of 360°?
If angle θ between two plane mirrors does not divide 360° exactly, the number of images N is the integer value of (360°/θ).
- N = Integer part of (360°/θ)
- Some images may overlap or coincide.
- This often appears in tricky exam questions on image formations with arbitrary angles.
8. Why do images sometimes appear laterally inverted in multiple mirror systems?
Lateral inversion occurs in mirror systems because reflection reverses the left-right orientation of objects.
- Each plane mirror produces a single inversion.
- With two or more reflections, the final image may revert or change orientation again.
- This concept is tested in mirror combination numericals and practical optics.
9. Is the mirror combination formula similar to the lens combination formula?
Yes, the formula for combination of mirrors is analogous to the combination of lenses:
1/f = 1/f1 + 1/f2
- Both use reciprocal addition for effective focal length.
- Mistakes often occur in sign conventions, so be careful during exams.
- This similarity appears frequently in JEE/Boards numerical problems.
10. Can we use the same formula for three or more mirrors?
For n mirrors in combination and in contact, the formula extends similarly:
1/f = 1/f1 + 1/f2 + 1/f3 + ... + 1/fn
- Apply sign convention for each mirror type.
- This principle helps solve advanced mirror system questions in competitive exams.
