Class 10 › Science › Chapter 9
Light: Reflection and Refraction
Laws of reflection, image formation by spherical mirrors, the mirror formula, refraction and refractive index, image formation by lenses, the lens formula and power of a lens.
1. Reflection of Light
- Light seems to travel in straight lines (a ray). A small source casts a sharp shadow of an opaque object. For very small objects, light bends around them (diffraction) and the ray model fails.
Laws of reflection
(i) Angle of incidence = angle of reflection.
(ii) The incident ray, the normal at the point of incidence and the reflected ray all lie in the same plane.
These apply to all reflecting surfaces, including spherical ones.
(ii) The incident ray, the normal at the point of incidence and the reflected ray all lie in the same plane.
These apply to all reflecting surfaces, including spherical ones.
Plane mirror image: virtual, erect, same size as the object, as far behind the mirror as the object is in front, and laterally inverted.
2. Spherical Mirrors and Important Terms
Concave
Curved inwards
Reflecting surface faces the centre of the sphere. Converges parallel rays; C and F are in front of the mirror.
Convex
Curved outwards
Diverges parallel rays; rays appear to come from F, which is behind the mirror (as is C).
| Term | Meaning |
|---|---|
| Pole (P) | Centre of the reflecting surface (on the mirror) |
| Centre of curvature (C) | Centre of the sphere the mirror is a part of; not on the mirror |
| Radius of curvature (R) | Radius of that sphere; PC = R |
| Principal axis | Line through P and C; normal to the mirror at P |
| Principal focus (F) | Point where rays parallel to the axis meet (concave) or appear to diverge from (convex) |
| Focal length (f) | Distance PF |
| Aperture | Diameter of the reflecting surface (taken much smaller than R) |
RelationR = 2f (F lies midway between P and C)
- A concave mirror held towards the Sun forms a tiny, bright, real, inverted image at F, which can burn paper (never look at the Sun through it).
3. Image Formation by Spherical Mirrors
| Concave mirror | |||
|---|---|---|---|
| Object position | Image position | Size | Nature |
| At infinity | At F | Highly diminished, point-sized | Real, inverted |
| Beyond C | Between F and C | Diminished | Real, inverted |
| At C | At C | Same size | Real, inverted |
| Between C and F | Beyond C | Enlarged | Real, inverted |
| At F | At infinity | Image not formed (parallel reflected rays) | |
| Between P and F | Behind the mirror | Enlarged | Virtual, erect |
| Convex mirror | |||
|---|---|---|---|
| Object position | Image position | Size | Nature |
| At infinity | At F, behind the mirror | Highly diminished, point-sized | Virtual, erect |
| Between infinity and P | Between P and F, behind the mirror | Diminished | Virtual, erect |
Uses: concave
Beams and magnifying
Torches, search-lights, headlights (powerful parallel beam); shaving mirrors and dentists' mirrors (enlarged image); solar furnaces (concentrate sunlight).
Uses: convex
Rear-view mirrors
Always give an erect, diminished image and have a wider field of view, so the driver sees a larger area than with a plane mirror.
- Concave mirror gives an erect and enlarged image only when the object is between P and F.
- A convex mirror can show a full-length image of a large object (Agra Fort mirror facing the Taj Mahal).
4. Ray Diagram Rules (Use Any Two)
| Incident ray | Concave mirror | Convex mirror |
|---|---|---|
| Parallel to principal axis | Reflects through F | Appears to diverge from F |
| Through F (concave) / directed towards F (convex) | Reflects parallel to axis | Reflects parallel to axis |
| Through C / directed towards C | Reflects back along same path (falls along the normal) | Reflects back along same path |
| Oblique ray at P | Reflects obliquely, making equal angles with the principal axis (laws of reflection) | |
- The image of a point is where two reflected rays intersect (real image), or where they appear to meet when extended backward (virtual image).
5. New Cartesian Sign Convention (Mirrors)
- Pole P is the origin; the principal axis is the x-axis.
- The object is always placed to the left of the mirror (light falls from the left).
- Distances along the axis are measured from the pole. Right of the origin: positive. Left: negative.
- Heights above the axis: positive. Below: negative.
| Quantity | Concave mirror | Convex mirror |
|---|---|---|
| Object distance u | Negative | Negative |
| Focal length f (and R) | Negative | Positive |
| Image distance v | Negative (real), positive (virtual) | Positive (virtual) |
6. Mirror Formula and Magnification
Mirror formula1/v + 1/u = 1/f (valid for all spherical mirrors, all object positions)
Magnificationm = h′/h = −v/u
h = object height (positive); h′ = image height (positive for virtual, negative for real images).
m negative → real, inverted. m positive → virtual, erect.
h = object height (positive); h′ = image height (positive for virtual, negative for real images).
m negative → real, inverted. m positive → virtual, erect.
Worked example 1 (convex mirror)
R = +3.00 m, so f = +1.50 m; bus at u = −5.00 m. 1/v = 1/f − 1/u = 1/1.5 + 1/5 = 6.5/7.5 → v = +1.15 m (behind the mirror).
m = −v/u = −(1.15)/(−5.00) = +0.23: image is virtual, erect and diminished (0.23 times).
Worked example 2 (concave mirror)
h = +4.0 cm, u = −25.0 cm, f = −15.0 cm. 1/v = 1/f − 1/u = −1/15 + 1/25 = −2/75 → v = −37.5 cm: screen 37.5 cm in front of the mirror; image real.
m = −v/u = −(−37.5)/(−25.0) = −1.5, so h′ = m × h = −6.0 cm: real, inverted and enlarged.
7. Refraction of Light
Refraction: change in the direction of light when it travels obliquely from one transparent medium to another, caused by a change in the speed of light.
- Everyday effects: a tank bottom appears raised; a pencil in water appears bent at the surface; letters under a glass slab appear raised; a lemon in water looks bigger; a coin hidden at the edge of a bowl becomes visible when water is poured in.
- Rarer to denser (air to glass or water): light slows down and bends towards the normal. Denser to rarer: speeds up and bends away from the normal.
- If the ray is incident normally (along the normal), it goes straight without bending.
- Rectangular glass slab: refraction at both faces is equal and opposite, so the emergent ray is parallel to the incident ray, only shifted sideways (lateral displacement).
Laws of refraction
(i) The incident ray, refracted ray and the normal lie in the same plane.
(ii) Snell's law: sin i / sin r = constant (for a given colour of light and given pair of media), 0 < i < 90°.
(ii) Snell's law: sin i / sin r = constant (for a given colour of light and given pair of media), 0 < i < 90°.
8. Refractive Index
Refractive index of medium 2 w.r.t. medium 1n₂₁ = v₁ / v₂ = sin i / sin r
Absolute refractive indexnm = c / v = (speed of light in vacuum) / (speed of light in the medium)
Absolute refractive indexnm = c / v = (speed of light in vacuum) / (speed of light in the medium)
- Speed of light in vacuum: c = 3 × 10⁸ m/s; in air it is marginally less; in glass or water it is considerably lower.
- Typical values: water 1.33, crown glass 1.52, kerosene 1.44, diamond 2.42 (highest in the table), air 1.0003 (lowest).
- Meaning of n = 2.42 (diamond): the ratio of the speed of light in vacuum to that in diamond is 2.42; light in diamond travels 2.42 times slower.
- Optical density: the medium with the larger refractive index is optically denser. This is not the same as mass density: kerosene is optically denser than water but has lower mass density. Light travels faster in the optically rarer medium.
- Worked example: glass n = 1.50 → v = c/n = 3 × 10⁸ / 1.50 = 2 × 10⁸ m/s.
- Air to water: light bends towards the normal (water is optically denser).
9. Refraction by Spherical Lenses
Convex lens
Converging
Bulges outward; thicker at the middle. Parallel rays meet at the principal focus on the other side. Focal length positive.
Concave lens
Diverging
Curved inward; thicker at the edges. Parallel rays appear to diverge from the principal focus on the same side. Focal length negative.
| Term | Meaning |
|---|---|
| Centres of curvature (C₁, C₂) | Centres of the two spheres forming the lens surfaces |
| Principal axis | Line through both centres of curvature |
| Optical centre (O) | Central point of the lens; a ray through it passes without deviation |
| Principal foci (F₁, F₂) | A lens has two foci, one on each side |
| Focal length (f) | Distance from the optical centre to the principal focus |
| Aperture | Effective diameter of the lens outline (taken small: thin lens) |
- A convex lens in sunlight forms a real image of the Sun at F; its distance from the lens gives the approximate focal length.
10. Image Formation by Lenses
| Convex lens | |||
|---|---|---|---|
| Object position | Image position | Size | Nature |
| At infinity | At F₂ | Highly diminished, point-sized | Real, inverted |
| Beyond 2F₁ | Between F₂ and 2F₂ | Diminished | Real, inverted |
| At 2F₁ | At 2F₂ | Same size | Real, inverted |
| Between F₁ and 2F₁ | Beyond 2F₂ | Enlarged | Real, inverted |
| At F₁ | At infinity | Image not formed | |
| Between F₁ and O | Same side as the object | Enlarged | Virtual, erect (magnifying glass) |
| Concave lens | |||
|---|---|---|---|
| Object position | Image position | Size | Nature |
| At infinity | At F₁ | Highly diminished, point-sized | Virtual, erect |
| Between infinity and O | Between F₁ and O | Diminished | Virtual, erect |
| Incident ray | Convex lens | Concave lens |
|---|---|---|
| Parallel to principal axis | Refracts through the other focus | Appears to diverge from the focus on the same side |
| Through focus (or directed towards it) | Emerges parallel to axis | Emerges parallel to axis |
| Through optical centre | Passes undeviated | Passes undeviated |
- A concave lens always gives a virtual, erect, diminished image, whatever the object position.
- For reading small print, use a convex lens of short focal length (5 cm); it acts as a magnifier when the object is within F.
- If half a convex lens is covered, it still forms a complete image (but dimmer), because every part of the lens forms the image.
11. Lens Formula, Magnification and Power
Lens formula1/v − 1/u = 1/f (distances from the optical centre; same sign convention as mirrors)
Magnificationm = h′/h = v/u (note: no minus sign for lenses)
m negative → real, inverted; m positive → virtual, erect.
m negative → real, inverted; m positive → virtual, erect.
Power of a lensP = 1/f (f in metres) SI unit: dioptre (D); 1 D = 1 m⁻¹
Convex: P positive. Concave: P negative.
Combination in contact: P = P₁ + P₂ + P₃ + …
Convex: P positive. Concave: P negative.
Combination in contact: P = P₁ + P₂ + P₃ + …
Worked example 3 (concave lens)
f = −15 cm, v = −10 cm. 1/u = 1/v − 1/f = −1/10 + 1/15 = −1/30 → u = −30 cm. m = v/u = +0.33 (erect, virtual, one-third size).
Worked example 4 (convex lens)
h = +2.0 cm, f = +10 cm, u = −15 cm. 1/v = 1/u + 1/f = −1/15 + 1/10 = 1/30 → v = +30 cm (other side). m = v/u = −2, h′ = −4.0 cm: real, inverted, enlarged.
- Power examples: +2.0 D → convex, f = +0.50 m. −2.5 D → concave, f = −0.40 m. Lens of f = 2 m (concave): P = −0.5 D.
- Lenses of powers +2.0 D and +0.25 D in contact equal a single lens of +2.25 D.
- Lens combinations are used in camera, microscope and telescope designs to reduce image defects.
12. Quick Revision
| Quantity | Mirror | Lens |
|---|---|---|
| Formula | 1/v + 1/u = 1/f | 1/v − 1/u = 1/f |
| Magnification | m = −v/u | m = v/u |
| f of concave | Negative | Negative |
| f of convex | Positive | Positive |
| Relation to R | f = R/2 | (P = 1/f) |
Common mistakes:
• Using the wrong sign for f: a concave mirror has f negative; a concave lens also has f negative.
• Using the mirror magnification (−v/u) for lenses or the lens form (v/u) for mirrors.
• Putting u as positive; the object is always on the left, so u is negative.
• Forgetting to convert f to metres before finding power.
• Saying denser medium means higher mass density; it means higher refractive index.
• Saying a convex mirror forms real images; it always forms virtual, erect, diminished images.
• Drawing the refracted ray at the slab's second face bending the wrong way: it bends away from the normal when going from glass to air.
• Using the wrong sign for f: a concave mirror has f negative; a concave lens also has f negative.
• Using the mirror magnification (−v/u) for lenses or the lens form (v/u) for mirrors.
• Putting u as positive; the object is always on the left, so u is negative.
• Forgetting to convert f to metres before finding power.
• Saying denser medium means higher mass density; it means higher refractive index.
• Saying a convex mirror forms real images; it always forms virtual, erect, diminished images.
• Drawing the refracted ray at the slab's second face bending the wrong way: it bends away from the normal when going from glass to air.