Concave and Convex Mirrors: f = R/2, Ray Diagrams, Real and Virtual Images (ICSE Class 8)

Understand Concave and Convex Mirrors: Image Formation and Uses

Concave and Convex Mirrors: Image Formation and Uses: formulas and key facts

Focal length

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

Same for concave and convex.

Concave mirror, real images

Object beyond C	image between F and C
Object at C	image at C
Object between C and F	image beyond C

All real and inverted.

Virtual images

Concave mirror with object between F and P | Convex mirror for every object

Erect, behind the mirror.

How to solve Concave and Convex Mirrors: Image Formation and Uses questions

1. 1Find $f=\frac{R}{2}$ and mark F at $f$ and C at $R$ from the pole.
2. 2Decide the object region: beyond C, at C, between C and F, at F, between F and P.
3. 3Use the table to state position, nature and size of the image.
4. 4For a diagram, draw two rays from the object tip with arrows and meet them at the image.

Concave and Convex Mirrors: Image Formation and Uses in real life

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.

Tricks to remember Concave and Convex Mirrors: Image Formation and Uses

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

• P-F-C

  Pole, Focus, Centre: in that order along the axis, F half-way to C.

  Use it when: Marking the axis.

• Beyond F is real

  Concave mirror, object beyond F: real and inverted. Inside F: virtual and erect.

  Use it when: Nature of image.

• Convex = always virtual

  Convex gives virtual, erect, small images for any object.

  Use it when: Convex mirror.

Concave and Convex Mirrors: Image Formation and Uses: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Where students lose marks in Concave and Convex Mirrors: Image Formation and Uses

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

• ✗Mistake: Calling every concave-mirror image real

  Inside F the image is virtual.

  Wrong working

  "Concave mirror: always a real, inverted image."

  Right working

  "Real and inverted beyond F; virtual and erect between F and P."

  ✓Do this: Check the position against F.

• ✗Mistake: Using f = 2R

  The focal length is half the radius.

  Wrong working

  $f=2\times 20=40$ cm.

  Right working

  $f=\frac{20}{2}=10$ cm.

  ✓Do this: F is half-way between P and C.

• ✗Mistake: No arrows in ray diagrams

  Arrows show the direction of light.

  Wrong working

  Lines without arrowheads.

  Right working

  Every ray carries an arrow.

  ✓Do this: Add arrows to each ray.

Practice questions on Concave and Convex Mirrors: Image Formation and Uses

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 · Very short answerBoard level

   State the nature of the image formed by a convex mirror.

   Hint

   For any object.

   Answer

   Virtual, erect and diminished (behind the mirror).

2. Q2 · 2 marks · Short answerBoard level

   A concave mirror has a focal length of 12 cm. Where is its centre of curvature? At what distance from the mirror must an object be placed so that the image is real, inverted and the same size as the object?

   Hint

   $R=2f$.

   Answer

   $R=24$ cm, so C is 24 cm from the pole. The image is the same size when the object is at C, i.e. 24 cm from the mirror.

3. Q3 · 3 marks · Short answerHarder board level

   An object is placed beyond the centre of curvature of a concave mirror. Describe the two rays you would draw from the top of the object, and state where the image forms and its nature.

   Hint

   Parallel ray and ray through C.

   Answer

   Draw a ray parallel to the principal axis, which reflects through F; and a ray through C, which returns along itself. They meet between F and C, giving a real, inverted, diminished image.

4. Q4 · 4 marks · Long answerHarder board level

   State which type of mirror you would use for (a) shaving, (b) a vehicle's side mirror, (c) a solar cooker, (d) a mirror at a sharp bend, giving a reason for each.

   Hint

   Think of the image needed.

   Answer

   (a) Concave: erect, magnified image at close range. (b) Convex: wide field of view. (c) Concave: concentrates sunlight at its focus. (d) Convex: wide view of oncoming traffic.

5. Q5 · 4 marks · Long answerHOTS / competency

   An object is 10 cm from a concave mirror of focal length 15 cm. (a) Where is the object relative to F? (b) State the nature of the image. (c) Can it be caught on a screen? (d) In which region must an object be placed to get a real image with a concave mirror?

   Hint

   Compare 10 cm with f.

   Answer

   (a) Between P and F. (b) Virtual, erect, magnified, behind the mirror. (c) No, a virtual image cannot be taken on a screen. (d) Beyond F (at any distance greater than the focal length).

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.Image of an object at C in a concave mirror?Show answer

   At C, real, inverted, same size.

3. 3.Which mirror gives a wide field of view?Show answer

   Convex.

4. 4.Nature of image inside F (concave)?Show answer

   Virtual, erect, magnified.

5. 5.Can a virtual image be taken on a screen?Show answer

   No.

Concave and Convex Mirrors: Image Formation and Uses: frequently asked questions