Spherical Mirrors ICSE Class 9: Concave and Convex Mirrors, Ray Diagrams and the Mirror Formula

What Spherical Mirrors is about

Weightage: CISCE publishes no chapter weightage and no question-paper layout for ICSE Class 9 Physics. Class IX is examined by your school: one 80-mark paper of 2 hours plus 20 marks of internal assessment. Spherical Mirrors is in the 6. Light (ii) part of the 2028 syllabus.Source: CISCE ICSE 2028 Physics syllabus, Class IX

Key concepts

Terms and f = R/2

• Pole $P$: the centre of the mirror's reflecting surface.
• Centre of curvature $C$: the centre of the sphere of which the mirror is a part.
• Radius of curvature $R$: the radius of that sphere ($PC$).
• Principal axis: the line through $P$ and $C$.
• Principal focus $F$: for a concave mirror, the point on the axis where rays parallel to the axis meet after reflection (real focus, in front); for a convex mirror, the point from which they appear to diverge (virtual focus, behind).
• Focal length $f$: the distance $PF$.
• Aperture: the width of the reflecting surface.

For mirrors of small aperture, $f=\frac{R}{2}$ (use without proof).

Worked example

A concave mirror has a radius of curvature of 30 cm. Find its focal length and the distance between $F$ and $C$.

Try it first, then show the solutionSolution

1. $f=\frac{30}{2}=15$ cm.
2. $FC=PC-PF=30-15=15$ cm.

Answer: 15 cm; 15 cm

Rules for drawing rays

Concave mirror:
1. A ray parallel to the principal axis passes **through $F$** after reflection.
2. A ray **through $F$ becomes parallel** to the axis.
3. A ray **through $C$ strikes the mirror normally and returns along the same path**.
4. A ray striking the pole reflects making an equal angle with the axis on the other side.

Convex mirror: the same rules, with 'through $F$' and 'through $C$' meaning directed towards $F$ or $C$ behind the mirror; reflected rays appear to come from $F$.

Parallel rays inclined to the axis meet (concave) or appear to diverge from (convex) a point on the focal plane, the plane through $F$ perpendicular to the axis.

Use any two rays to locate an image.

Worked example

In a ray diagram for a concave mirror, a ray from the top of an object passes through $C$. What happens to it, and why?

Try it first, then show the solutionSolution

1. A ray through $C$ lies along a radius, so it meets the mirror along the normal ($i=0°$).
2. It is reflected straight back along the same path.

Answer: It retraces its path, because it strikes the mirror normally.

Images formed by a concave mirror

As the object moves from far away towards the mirror:

• At infinity: image at $F$; real, inverted, highly diminished (point-sized).
• **Beyond $C$**: image between $F$ and $C$; real, inverted, diminished.
• **At $C$**: image at $C$; real, inverted, same size.
• **Between $C$ and $F$**: image beyond $C$; real, inverted, magnified.
• **At $F$**: image at infinity; real, inverted, highly magnified.
• **Between $F$ and $P$: image behind the mirror; virtual, erect, magnified**.

Only the last case gives a virtual image. Real images are always inverted and can be caught on a screen.

Worked example

Where should an object be placed in front of a concave mirror to get (a) a real image of the same size (b) a virtual, magnified image?

Try it first, then show the solutionSolution

1. (a) At $C$ (twice the focal length).
2. (b) Between $F$ and $P$.

Answer: (a) at C (b) between F and P

Images formed by a convex mirror

For a convex mirror, wherever the object is placed in front of it, the image is:

• formed behind the mirror, between $P$ and $F$;
• virtual, erect and diminished.

As the object moves from infinity towards the mirror, the image moves from $F$ towards $P$ and grows (but is always smaller than the object).

A convex mirror gives a wide field of view, which is why it is used as a rear-view mirror and for security in shops.

Worked example

A car's rear-view mirror is convex. State two features of the image of a following car, and one disadvantage.

Try it first, then show the solutionSolution

1. Image is erect (upright) and diminished, so a wide area fits in the mirror.
2. Disadvantage: the diminished image makes the car seem further away than it is.

Answer: Erect and diminished; distances look larger than they are.

Cartesian sign convention and the mirror formula

Cartesian sign convention (object on the left, light travelling left to right):

• all distances are measured from the pole;
• distances in the direction of the incident light (to the right) are positive; against it (to the left) are negative;
• heights above the axis are positive, below negative.

So the object distance $u$ is negative; a concave mirror's $f$ is negative; a convex mirror's $f$ is positive; a real image (in front) has negative $v$; a virtual image (behind) has positive $v$.

Mirror formula: $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ (no derivation).

Magnification: $m=\frac{h_2}{h_1}=-\frac{v}{u}$. Negative $m$: real, inverted; positive $m$: virtual, erect; $|m|>1$: magnified.

Worked example

An object is 30 cm in front of a concave mirror of focal length 10 cm. Find the position and nature of the image and the magnification.

Try it first, then show the solutionSolution

1. $u=-30$ cm, $f=-10$ cm.
2. $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=-\frac{1}{10}+\frac{1}{30}=-\frac{2}{30}$, so $v=-15$ cm.
3. $m=-\frac{v}{u}=-\frac{-15}{-30}=-0.5$: real, inverted, half size, 15 cm in front of the mirror.

Answer: v = −15 cm; m = −0.5

Uses of spherical mirrors

Concave mirror:

• shaving and make-up mirror: face within $f$ gives an erect, magnified image;
• dentist's mirror: magnified view of teeth;
• reflector in torches, car headlights and searchlights: bulb at $F$ gives a parallel beam;
• solar furnaces and cookers: sunlight converged at $F$ produces high temperature;
• doctors' head mirrors to focus light into the ear, nose or throat.

Convex mirror:

• rear-view mirror in vehicles: erect image and wide field of view;
• security mirrors in shops and at sharp road bends;
• street-light reflectors to spread light over a wide area.

Worked example

Why is the bulb of a torch placed at the focus of its concave reflector?

Try it first, then show the solutionSolution

1. Rays from $F$ become parallel to the principal axis after reflection.
2. So the torch gives a strong parallel beam that does not spread much.

Answer: To get a parallel beam of light.

Physics in real life: Spherical Mirrors

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Images Formed by Concave and Convex Mirrors: Ray Rules and Nature of Images
• Mirror Formula, Cartesian Sign Convention and Magnification

Spherical Mirrors formula sheet

Focal length

$f=\frac{R}{2}$

No proof required.

Mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Use signs; no derivation.

Magnification

$m=\frac{h_2}{h_1}=-\frac{v}{u}$

m < 0 real, inverted; m > 0 virtual, erect.

Sign of f

$f_{concave}<0;f_{convex}>0$

Cartesian convention.

Object distance

$u<0$

Object in front (left).

Spherical Mirrors: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Spherical Mirrors

The question patterns to expect, and the method that works for each.

Tricks to remember Spherical Mirrors

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Concave caves in, converges

  Concave mirrors are hollow like a cave and make parallel light converge.

  Use it when: Which mirror is which.

• PF CC

  Parallel → Focus; Focus → parallel; Centre → Comes back.

  Use it when: Ray rules.

• Convex is always VED

  Convex mirror image is always Virtual, Erect, Diminished.

  Use it when: Convex image questions.

• Minus m, real thing

  Negative magnification: real and inverted. Positive: virtual and erect.

  Use it when: Reading formula answers.

Spherical Mirrors: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 9-mark question split into 3 + 3 + 3 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Spherical Mirrors

The slips examiners see most often, and what to write instead.

• ✗Mistake: Dropping signs in the mirror formula

  Substituting $u=30$ and $f=10$ for a concave mirror gives the wrong image position and nature.

  Wrong working

  $\frac{1}{v}=\frac{1}{10}-\frac{1}{30}$

  Right working

  $\frac{1}{v}=-\frac{1}{10}+\frac{1}{30}$

  ✓Do this: Write 'u = −…, f = −… (concave)' before substituting.

  Usually costs: Most of the question.

• ✗Mistake: No arrows or dotted lines in ray diagrams

  Rays without arrows, or solid lines behind a mirror, lose diagram marks.

  ✓Do this: Arrows on real rays; dotted extensions behind the mirror.

  Usually costs: 1 mark.

• ✗Mistake: Wrong focus for a convex mirror

  Students draw reflected rays passing through a point in front of a convex mirror.

  ✓Do this: For a convex mirror, rays only appear to come from F behind it.

  Usually costs: 1 mark.

• ✗Mistake: Not interpreting the answer

  Giving $v=+30$ cm without saying 'virtual, behind the mirror'.

  ✓Do this: Translate the signs of v and m into words.

  Usually costs: 1 mark.

• ✗Mistake: Attempting a scale drawing or derivation

  Scale drawings and the derivation of the mirror formula are not required in Class IX.

  ✓Do this: Draw neat, proportional sketches; use the formula directly.

  Usually costs: Time.

Practice questions on Spherical Mirrors

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   The image formed by a convex mirror is always:
   (a) real and inverted
   (b) virtual, erect and diminished
   (c) virtual, erect and magnified
   (d) real and same size

   Hint

   VED.

   Answer

   (b)

2. Q2 · 1 mark · MCQExam level

   A concave mirror forms a real image of the same size when the object is at:
   (a) F
   (b) C
   (c) between F and P
   (d) infinity

   Hint

   u = 2f.

   Answer

   (b)

3. Q3 · 1 mark · Short answerExam level

   The radius of curvature of a convex mirror is 40 cm. State its focal length with sign (Cartesian convention).

   Hint

   f = R/2, convex positive.

   Answer

   $f=+20$ cm.

4. Q4 · 1 mark · Assertion-reasonHarder exam level

   Assertion (A): A concave mirror is used in torches.
   Reason (R): Light from a bulb placed at the focus of a concave mirror becomes a parallel beam after reflection.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   Ray through F → parallel.

   Answer

   (c)

5. Q5 · 3 marks · Short answerHarder exam level

   An object is placed 12 cm in front of a convex mirror of focal length 12 cm. Find the image position and magnification.

   Hint

   u = −12, f = +12.

   Answer

   $\frac{1}{v}=\frac{1}{12}+\frac{1}{12}=\frac{1}{6}$, $v=+6$ cm (behind); $m=+0.5$: virtual, erect, half size.

6. Q6 · 3 marks · Short answerHarder exam level

   An object is 40 cm in front of a concave mirror of radius of curvature 30 cm. Find the image distance and magnification, and describe the image.

   Hint

   f = −15 cm.

   Answer

   $\frac{1}{v}=-\frac{1}{15}+\frac{1}{40}=-\frac{5}{120}$, $v=-24$ cm; $m=-0.6$: real, inverted, diminished, 24 cm in front.

7. Q7 · 3 marks · Short answerHarder exam level

   Draw a ray diagram for an object at infinity for a concave mirror (parallel rays inclined to the axis) and state where the image forms.

   Hint

   Focal plane.

   Answer

   Parallel rays inclined to the axis meet after reflection at a point in the focal plane (the plane through F perpendicular to the axis). The image is real, inverted and point-sized there.

8. Q8 · 3 marks · Short answerHarder exam level

   A concave mirror forms a real image four times larger than the object on a screen 1.2 m from the mirror. Find the object distance and the focal length.

   Hint

   m = −4, v = −120 cm.

   Answer

   $-4=-\frac{-120}{u}$, so $u=-30$ cm. $\frac{1}{f}=-\frac{1}{120}-\frac{1}{30}=-\frac{5}{120}$, $f=-24$ cm.

9. Q9 · 2 marks · Short answerExam level

   Give one use each of a concave and a convex mirror with a reason.

   Hint

   Image property.

   Answer

   Concave: shaving mirror (erect, magnified image when the face is within F). Convex: rear-view mirror (erect, diminished image with a wide field of view).

10. Q10 · 4 marks · Long answerHarder exam level

    An object moves from 5 cm to 25 cm in front of a concave mirror of focal length 10 cm. Describe how the image changes, with positions at u = −5 cm and u = −25 cm.

    Hint

    Use the formula at both ends.

    Answer

    At $u=-5$: $\frac{1}{v}=-\frac{1}{10}+\frac{1}{5}=\frac{1}{10}$, $v=+10$ cm, $m=+2$ (virtual, erect, ×2). At $u=-25$: $\frac{1}{v}=-\frac{1}{10}+\frac{1}{25}=-\frac{3}{50}$, $v\approx -16.7$ cm, $m\approx -0.67$ (real, inverted, diminished). Passing through F (at 10 cm) the image jumps from behind the mirror to infinity and back in front.

11. Q11 · 2 marks · Short answerHOTS / competency

    Why can a convex mirror not be used to make a solar cooker, while a concave mirror can?

    Hint

    Converge or diverge.

    Answer

    A concave mirror converges parallel sunlight to a real focus, concentrating heat on the pot. A convex mirror spreads the light out from a virtual focus, so no point is heated strongly.

12. Q12 · 3 marks · Short answerHOTS / competency

    You are given a concave mirror and a convex mirror that look alike. Suggest two simple tests to tell them apart without measuring.

    Hint

    Images of near and far objects.

    Answer

    (1) Look at your face close up: a concave mirror gives an erect, magnified image; a convex one gives an erect, diminished image. (2) Focus sunlight or a distant window onto paper: only the concave mirror forms a real image on the paper.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Relation between f and R?Show answer

   f = R/2.

2. 2.What happens to a ray through C of a concave mirror?Show answer

   It returns along the same path.

3. 3.Where should the object be for a same-size real image with a concave mirror?Show answer

   At C.

4. 4.Nature of a convex mirror's image?Show answer

   Virtual, erect, diminished.

5. 5.Write the mirror formula.Show answer

   1/v + 1/u = 1/f.

6. 6.What does a negative magnification mean?Show answer

   The image is real and inverted.

7. 7.Sign of f for a concave mirror (Cartesian)?Show answer

   Negative.

8. 8.Name two uses of concave mirrors.Show answer

   Shaving mirrors and headlight reflectors (also solar cookers, dentists' mirrors).

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you define P, C, R, F and f?
• ☐Can you state the four ray rules?
• ☐Can you draw diagrams for all object positions of a concave mirror?
• ☐Do you know the convex mirror image is always VED?
• ☐Do you put signs into the mirror formula?
• ☐Can you interpret signs of v and m?
• ☐Can you give uses with reasons?

Spherical Mirrors: frequently asked questions