Quick Summary
Optics studies the behaviour of light — reflection from mirrors and refraction through lenses. For Tamil Nadu board exams, you must be able to draw ray diagrams, apply mirror and lens formulae with sign convention, and answer defects-of-vision questions. This chapter has both theory and numericals every year.
Key Definitions
- Reflection: Bouncing back of light into the same medium after hitting a surface.
- Refraction: Bending of light as it passes from one medium to another due to change in speed.
- Principal axis: The straight line passing through the pole and centre of curvature of a mirror or lens.
- Principal focus (F): Point where parallel rays converge (concave) or appear to diverge from (convex) after reflection/refraction.
- Focal length (f): Distance between the focus and the pole (mirror) or optical centre (lens).
- Centre of curvature (C): Centre of the sphere of which the mirror forms a part. C = 2f from the pole.
- Optical centre: The central point of a lens through which light passes without bending.
- Magnification (m): Ratio of image height to object height. Also m = −v/u (mirrors) or m = v/u (lenses).
Formulae Reference
| Concept | Formula | Notes |
|---|---|---|
| Mirror formula | 1/v + 1/u = 1/f | All distances from pole |
| Lens formula | 1/v − 1/u = 1/f | All distances from optical centre |
| Mirror magnification | m = −v/u = h₂/h₁ | Negative m → inverted image |
| Lens magnification | m = v/u = h₂/h₁ | Negative m → inverted image |
| Refractive index | n = c/v = sin i / sin r | c = speed of light in vacuum |
| Power of lens | P = 1/f (f in metres) | Unit: dioptre (D) |
Sign Convention (New Cartesian)
All distances are measured from the pole (mirror) or optical centre (lens).
- Distances measured in the direction of incident light → positive (+)
- Distances measured opposite to incident light → negative (−)
For a standard setup (light coming from the left):
- Object distance u is always negative (object is on the left of the mirror/lens)
- For real images: v is negative (mirror) or positive (lens)
- For virtual images: v is positive (mirror) or negative (lens)
- Concave mirror: f is negative | Convex mirror: f is positive
- Convex lens: f is positive | Concave lens: f is negative
Laws of Reflection
1. The angle of incidence (∠i) equals the angle of reflection (∠r). 2. The incident ray, reflected ray, and normal at the point of incidence all lie in the same plane.
Both laws apply to plane mirrors, concave mirrors, and convex mirrors.
Laws of Refraction (Snell's Law)
1. The incident ray, refracted ray, and normal at the point of incidence all lie in the same plane. 2. Snell's Law: n₁ sin i = n₂ sin r (ratio of sines is constant).
Key behaviour:
- Light entering a denser medium (glass, water) bends towards the normal.
- Light entering a rarer medium (air from glass) bends away from the normal.
Why does a pencil look bent in water? Light from the submerged part of the pencil bends away from the normal as it enters the less dense air. Our eyes trace the light back in a straight line, making the pencil appear bent at the water surface.
Image Formation — Concave Mirror Summary
| Object position | Image position | Nature |
|---|---|---|
| At infinity | At F | Real, inverted, highly diminished |
| Beyond C | Between F and C | Real, inverted, diminished |
| At C | At C | Real, inverted, same size |
| Between F and C | Beyond C | Real, inverted, magnified |
| At F | At infinity | Real, inverted, highly magnified |
| Between F and P (pole) | Behind mirror | Virtual, erect, magnified |
Image Formation — Convex Lens Summary
| Object position | Image position | Nature |
|---|---|---|
| At infinity | At F₂ | Real, inverted, highly diminished |
| Beyond 2F₁ | Between F₂ and 2F₂ | Real, inverted, diminished |
| At 2F₁ | At 2F₂ | Real, inverted, same size |
| Between F₁ and 2F₁ | Beyond 2F₂ | Real, inverted, magnified |
| At F₁ | At infinity | — |
| Between F₁ and O | Same side as object | Virtual, erect, magnified |
Worked Numerical Examples
Example 1 — Concave Mirror (Object Beyond C)
Problem: An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the image distance, magnification, and nature of the image.
Example 2 — Convex Lens (Object Beyond 2F)
Problem: An object is placed 25 cm from a convex lens of focal length 15 cm. Find the image position and magnification.
Example 3 — Power of a Lens
Problem: A person needs spectacles of power +2 D. Find the focal length and identify the type of lens and the vision defect.
Example 4 — Interpreting Magnification
Problem: The magnification produced by a mirror is +2. What does this tell you about the image?
Example 5 — Concave Mirror Numerical (Full)
Problem: An object is placed 45 cm in front of a concave mirror of focal length 15 cm. Find the image position, magnification, and describe the image fully.
Board Exam Q&A — Model Answers
One Mark Questions
Q: Define refraction of light. A: Refraction is the bending of light when it passes from one transparent medium to another, due to a change in its speed.
Q: What is the focal length of a lens of power 4 D? A: f = 1/P = 1/4 = 0.25 m = 25 cm. (Convex lens — positive power.)
Q: State one use of a convex mirror. A: Convex mirrors are used as rear-view mirrors in vehicles because they provide a wider field of view and always form an erect, diminished virtual image.
Q: What is magnification? What does a negative magnification indicate? A: Magnification is the ratio of image height to object height (m = h₂/h₁). A negative magnification means the image is inverted (real image for mirrors, real image for lenses).
Two Mark Questions
Q: State the laws of reflection. A: 1. The angle of incidence is equal to the angle of reflection (∠i = ∠r). 2. The incident ray, reflected ray, and normal at the point of incidence all lie in the same plane.
Q: Differentiate between a real image and a virtual image.
| Property | Real Image | Virtual Image |
|---|---|---|
| Formation | Rays actually converge | Rays appear to diverge |
| Can be caught on screen? | Yes | No |
| Nature | Inverted | Erect |
| Example | Cinema projector, camera | Plane mirror, magnifying glass |
Q: Why does a pencil appear bent when placed in a glass of water? A: Light from the submerged part of the pencil travels from water (denser medium) to air (rarer medium). It bends away from the normal at the surface. Our eyes trace this refracted light back in a straight line, so the pencil appears to be bent at the water surface. This is due to refraction.
Five Mark Questions
Q: Explain the image formation by a concave mirror for an object placed at different positions.
A concave mirror converges light. As the object moves from infinity towards the pole: 1. Object at infinity: Parallel rays converge at F. Image at F — real, inverted, point-sized. 2. Object beyond C: Image between F and C — real, inverted, diminished. 3. Object at C: Image at C — real, inverted, same size. (Used in: no practical use, but important theoretically) 4. Object between F and C: Image beyond C — real, inverted, magnified. (Used in: projectors) 5. Object at F: Reflected rays are parallel — image at infinity. 6. Object between F and P: Image behind mirror — virtual, erect, magnified. (Used in: shaving/makeup mirror)
Q: Derive the mirror formula 1/v + 1/u = 1/f.
Consider a concave mirror with pole P, focus F, and centre of curvature C. Let an object AB be placed in front of the mirror. The image A'B' is formed by reflection.
Using similar triangles formed by the two reflected rays:
Defects of Vision — Complete Table
| Defect | What the person cannot see | Cause | Correcting lens |
|---|---|---|---|
| Myopia (near-sightedness) | Distant objects clearly | Image forms in front of retina (eyeball too long) | Concave (diverging) lens |
| Hypermetropia (far-sightedness) | Nearby objects clearly | Image forms behind retina (eyeball too short) | Convex (converging) lens |
| Presbyopia | Both near and far with age | Loss of flexibility of eye lens with age | Bifocal lens (both concave + convex) |
Exam tip: Always link the defect to the correcting lens AND explain why:
- Myopia → concave lens → diverges light so image moves back onto retina.
- Hypermetropia → convex lens → converges light so image moves forward onto retina.
Common Board Exam Mistakes
correct signs before substituting.
difference.
points: P, F, C (or 2F), object, image, arrowheads.
- Forgetting sign convention: u is always negative for real objects. Practice writing u, v, and f with
- Mixing mirror and lens formulae: Mirror:
1/v + 1/u = 1/f. Lens:1/v − 1/u = 1/f. Note the − sign - Small or unlabelled ray diagrams: Examiners deduct marks for small diagrams. Draw large and label all
- Writing image nature without all three properties: Always state position + size + erect/inverted.
- Concave vs convex confusion: Remember — concave mirror caves inward; convex bulges outward.
Tamil Nadu Board Exam Pattern
- Chapter weightage: 6–8 marks
- Five-mark: Usually 1 five-mark on image formation table (concave mirror) OR mirror formula derivation.
- Two-mark: Differentiate real vs virtual image; laws of reflection; pencil-in-water question.
- Numericals: At least 1 numerical using mirror or lens formula — practice Examples 1, 2, and 5 above.
- Defects of vision: Almost certain in 2-mark or as part of a 5-mark — memorise the full table.
Revision Checklist
- Sign convention: u negative, f negative for concave mirror, f positive for convex lens
- Mirror formula
1/v + 1/u = 1/fand lens formula1/v − 1/u = 1/fmemorised - Image formation table for concave mirror (6 positions) prepared
- Defects-of-vision table (3 defects, cause, lens) prepared
- Laws of reflection and refraction stated clearly
- Real vs virtual image differences memorised
- All five worked numericals solved independently without looking at solutions