Physics Class 12 Part II…
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Reflection Spherical Mirrors

🎓 Class 12 Physics CBSE Theory Ch 9 – Ray Optics and Optical Instruments ⏱ ~14 min
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આ MCQ મોડ્યુલ આના પર આધારિત છે: Reflection Spherical Mirrors

આ મૂલ્યાંકન આના પર આધારિત હશે: Reflection Spherical Mirrors

મૂલ્યાંકન બનાવવામાં તેમની સામગ્રી સામેલ કરવા ચિત્રો, PDF અથવા Word દસ્તાવેજ અપલોડ કરો.

Reflection Spherical Mirrors

9.1 Introduction — Light and the Ray Model

Light is an electromagnetic wave that can travel through vacuum at the extraordinary speed \(c = 3\times 10^8\) m/s. Yet for most everyday optics — from shaving mirrors to camera lenses and telescopes — we do not need the full wave description. When the wavelength of light \(\lambda\) (around 400–700 nm) is much smaller than the openings and obstacles it encounters (mirrors, lenses, apertures of a few centimetres or more), the light simply travels in straight lines called rays.

What you will learn in Part 1: Laws of reflection, the geometry of concave and convex mirrors, the Cartesian sign convention, the mirror formula, magnification, and image formation for all standard object positions.

9.2 Reflection of Light by Spherical Mirrors

When a ray of light meets a polished surface, it bounces back. The two famous laws of reflection were known long before Newton:

  1. The angle of incidence equals the angle of reflection: \(\angle i = \angle r\).
  2. The incident ray, the reflected ray and the normal to the surface at the point of incidence all lie in one plane.

These laws hold at every single point on a curved mirror — the normal, of course, is along the local radius of curvature.

Geometry of a Spherical Mirror

A spherical mirror is a slice cut from a hollow sphere whose inner or outer surface has been silvered. If the inside of the bowl reflects, the mirror is concave (converging). If the outside reflects, it is convex (diverging).

Concave Mirror P F C principal axis Convex Mirror P F C principal axis
Fig 9.1: Concave mirror (centre and focus on reflecting side) vs convex mirror (centre and focus behind the mirror).

Key Terms

  • Pole (P): the geometric centre of the reflecting surface.
  • Centre of curvature (C): the centre of the sphere of which the mirror is a part.
  • Principal axis: the line PC extended.
  • Radius of curvature (R): the distance PC.
  • Principal focus (F): the point on the axis where rays parallel to the axis converge (concave) or appear to diverge from (convex) after reflection.
  • Focal length (f): the distance PF.
Key relation: For small-aperture (paraxial) mirrors, \(f = R/2\). The focus lies exactly midway between the pole and the centre of curvature.

Cartesian Sign Convention

  1. All distances are measured from the pole (P).
  2. Distances measured in the direction of the incident light → positive (+).
  3. Distances measured opposite to the incident light → negative (–).
  4. Heights above the principal axis → positive; below → negative.

Consequences: for a real object in front of a mirror, \(u < 0\). For a concave mirror, \(f < 0\) and \(R < 0\). For a convex mirror, \(f > 0\) and \(R > 0\).

The Mirror Formula and Magnification

\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\]

where \(u\) is the object distance, \(v\) the image distance and \(f\) the focal length. The lateral magnification is

\[m = \frac{h'}{h} = -\frac{v}{u}\]

A positive \(m\) means an erect image; negative means inverted. \(|m|>1\) magnified, \(|m|<1\) diminished.

Image Formation by a Concave Mirror — Six Cases

Object PositionImage PositionNatureSize
At infinityAt FReal, invertedHighly diminished (point)
Beyond CBetween F and CReal, invertedDiminished
At CAt CReal, invertedSame size
Between C and FBeyond CReal, invertedMagnified
At FAt infinityReal, invertedHighly magnified
Between F and PBehind mirrorVirtual, erectMagnified
1. Object at infinity F P 2. Beyond C C F 3. At C C 4. Between C and F C F 5. At F F 6. Between F and P (virtual) virtual F
Fig 9.2: Six standard ray diagrams for a concave mirror — cases 1–5 give real images, case 6 a virtual magnified image (shaving/make-up mirror).

Image Formation by a Convex Mirror

Whatever the object distance, a convex mirror always produces a virtual, erect and diminished image lying between the pole and the focus behind the mirror. This gives a much wider field of view than a plane mirror — the reason all vehicle side-view mirrors and many shopping-mall surveillance mirrors are convex.

O I P F C
Fig 9.3: A convex mirror always gives a virtual, erect, diminished image between P and F behind the mirror.

Uses of Spherical Mirrors

  • Concave: shaving/make-up mirrors (object within focal length → magnified erect), dental mirrors, reflectors in torches/headlamps, solar concentrators, astronomical (reflecting) telescope primary mirrors.
  • Convex: vehicle rear-view and side-view mirrors, blind-corner traffic mirrors, supermarket surveillance — all exploit the wide field of view.

Worked Examples — Spherical Mirrors

Example 1: Concave mirror, object within focal length

An object is placed 10 cm in front of a concave mirror of focal length 15 cm. Find the position, size and nature of the image if the object is 2 cm tall.

Given \(u = -10\) cm, \(f = -15\) cm, \(h = +2\) cm. \[\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-15} - \frac{1}{-10} = -\frac{1}{15} + \frac{1}{10} = \frac{-2+3}{30} = \frac{1}{30}\] So \(v = +30\) cm (behind the mirror → virtual). \[m = -\frac{v}{u} = -\frac{30}{-10} = +3 \quad\Rightarrow\quad h' = m\cdot h = +6\,\text{cm}\] Image is virtual, erect and magnified three-fold — the familiar shaving-mirror configuration.

Example 2: Concave mirror, object beyond C

A 5 cm tall object stands 40 cm in front of a concave mirror with \(R = 30\) cm. Locate and describe the image.

\(f = R/2 = -15\) cm, \(u = -40\) cm. \[\frac{1}{v} = \frac{1}{-15} - \frac{1}{-40} = \frac{-8+3}{120} = -\frac{5}{120}\] \(v = -24\) cm. \(m = -v/u = -(-24)/(-40) = -0.6\). \(h' = -3\) cm. Real, inverted, diminished image at 24 cm in front of the mirror.

Example 3: Convex car side mirror

A convex rear-view mirror of focal length 2 m shows the image of a truck 10 m behind. Find the image distance and magnification.

\(f = +2\) m, \(u = -10\) m. \[\frac{1}{v} = \frac{1}{2} - \frac{1}{-10} = \frac{1}{2} + \frac{1}{10} = \frac{6}{10}\] \(v = +1.67\) m (behind the mirror). \(m = -v/u = -1.67/(-10) = +0.167\). Virtual, erect, about 1/6 the truck's height — hence "objects in mirror are closer than they appear".

Example 4: Find f from real image data

A concave mirror forms a real image three times the size of the object when the object is at 20 cm. Find \(f\).

Real image ⇒ \(m = -3\) (inverted). \(m = -v/u \Rightarrow v = 3u = -60\) cm (\(u=-20\) cm). \[\frac{1}{f} = \frac{1}{v}+\frac{1}{u} = \frac{1}{-60}+\frac{1}{-20} = -\frac{4}{60}\] \(\boxed{f = -15\ \text{cm}}\).

Example 5: Image at the object's position

At what distance must an object be placed in front of a concave mirror of \(R=24\) cm so that image forms at the object's own location?

Image coincides with object ⇒ object is at C. \(u = -R = -24\) cm. Placed 24 cm in front of the mirror.

Example 6: Convex mirror — field of view

A convex mirror of focal length 20 cm forms the image of a 5 m tall pole at 3 m from the mirror. How tall does the pole appear?

\(u=-3\) m, \(f=+0.20\) m. \[\frac{1}{v} = \frac{1}{0.20} - \frac{1}{-3} = 5 + 0.333 = 5.333\quad\Rightarrow v=0.1875\text{ m}\] \(m = -v/u = 0.0625\). \(h' = 0.0625\times 5 = 0.31\) m ≈ 31 cm. Virtual, erect, greatly diminished — typical of a wide-angle convex mirror.
Activity — Burn Paper with a Concave MirrorL3 Apply
Predict: If you hold a small concave mirror in bright sunlight and move a piece of paper in front of it, at what distance will the paper start to smoke or catch fire?
  1. Take a concave mirror (a shaving mirror works) outdoors in direct sunlight.
  2. Hold a sheet of dry paper in front of the mirror's reflecting side.
  3. Slide the paper towards and away from the mirror until you see the smallest, brightest spot of light.
  4. Measure the distance from the mirror to that spot with a ruler.
Observation: The paper smokes (and may ignite) when the bright spot is smallest.

Explanation: The Sun is effectively at infinity, so parallel rays converge at the principal focus. The distance from mirror to bright spot is therefore the focal length \(f\). All the sunlight intercepted by the mirror's aperture is concentrated into a tiny area, raising the temperature above the paper's ignition point.

Interactive: Mirror Ray Diagram Calculator L3 Apply

Choose mirror type, pick object distance (cm) and focal length magnitude (cm). The calculator applies the mirror formula with the Cartesian sign convention.

Competency-Based Questions

A driver uses a convex rear-view mirror of focal length 3 m. A bike is following the car at 15 m behind the mirror. The driver is curious about image properties and how the mirror formula applies.

Q1. L1 Remember For a convex mirror with the Cartesian convention, the focal length is:

  • A. Negative
  • B. Positive
  • C. Zero
  • D. Depends on object
Answer: B. The focus lies behind the mirror, on the side opposite to the incident light, so \(f > 0\).

Q2. L3 Apply Find the image distance for the bike. (3 marks)

\(u=-15\) m, \(f=+3\) m. \(\frac{1}{v}=\frac{1}{3}+\frac{1}{15}=\frac{6}{15}\), \(v=+2.5\) m behind the mirror.

Q3. L2 Understand Why are convex mirrors preferred as vehicle rear-view mirrors despite the diminished image?

They produce an always-erect virtual image and, because rays diverge after reflection, the field of view is much wider than a plane or concave mirror of the same aperture. A smaller image accommodates a large traffic scene at a glance.

Q4. L4 Analyse A concave mirror produces an image exactly the same size as the object. Where is the object? Justify. (2 marks)

At the centre of curvature C. Then \(u=v=-R\) and \(|m|=1\) with an inverted image at the same location as the object.

Q5. L5 Evaluate Assertion: Concave mirrors are used as shaving mirrors because they produce magnified images. Evaluate this claim. (3 marks)

Correct, but the key condition is that the face be placed within the focal length. Then the image is virtual, erect and magnified. Placed beyond F, the mirror forms a real inverted image — useless for shaving. So the mirror type is necessary but not sufficient; placement matters.

Assertion-Reason Questions

Assertion (A): The focal length of a spherical mirror is half the radius of curvature.

Reason (R): This relation holds only for paraxial rays close to the principal axis.

  • A. Both A and R true; R is the correct explanation.
  • B. Both true; R not the correct explanation.
  • C. A true, R false.
  • D. A false, R true.
Answer: A. \(f=R/2\) is derived under the small-angle (paraxial) approximation; wide-aperture mirrors show spherical aberration.

Assertion (A): A convex mirror always forms a virtual image.

Reason (R): Reflected rays diverge and only their backward extensions meet.

  • A. Both true; R is correct explanation.
  • B. Both true; R not correct explanation.
  • C. A true, R false.
  • D. A false, R true.
Answer: A. Because rays from any real object diverge after reflection from a convex surface, the image can only be reconstructed by extending rays behind the mirror — hence virtual.

Assertion (A): A concave mirror can form both real and virtual images.

Reason (R): The nature of the image depends on whether the object lies inside or outside the focal length.

  • A. Both true; R is correct explanation.
  • B. Both true; R not correct explanation.
  • C. A true, R false.
  • D. A false, R true.
Answer: A. Object between F and P → virtual erect magnified; beyond F → real inverted.

Frequently Asked Questions - Reflection Spherical Mirrors

What is the main concept covered in Reflection Spherical Mirrors?
In NCERT Class 12 Physics Chapter 9 (Ray Optics and Optical Instruments), "Reflection Spherical Mirrors" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Reflection Spherical Mirrors useful in real-life applications?
Real-life applications of "Reflection Spherical Mirrors" from NCERT Class 12 Physics Chapter 9 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Reflection Spherical Mirrors?
Key formulas in "Reflection Spherical Mirrors" (NCERT Class 12 Physics Chapter 9 Ray Optics and Optical Instruments) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 9?
NCERT Class 12 Physics Chapter 9 (Ray Optics and Optical Instruments) is structured so each part builds on the previous one. "Reflection Spherical Mirrors" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Reflection Spherical Mirrors?
CBSE board questions from "Reflection Spherical Mirrors" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Reflection Spherical Mirrors" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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Physics Class 12 Part II – NCERT (2025-26)
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