Class 10 Science : Light: Reflection and Refraction Notes
1. Basic Idea of Light
- Light generally travels in straight-line paths in a uniform medium.
- We see an object when light from the object reaches our eyes.
- Two major phenomena studied in this chapter:
- Reflection — bouncing back of light from a surface.
- Refraction — change in direction of light when it passes obliquely from one transparent medium to another.
PART A — REFLECTION OF LIGHT
2. Laws of Reflection
There are two important laws:
- Angle of incidence = Angle of reflection
i=r - The incident ray, reflected ray and normal at the point of incidence lie in the same plane.
These laws apply to plane as well as spherical reflecting surfaces.
Plane Mirror — Image Characteristics
A plane mirror produces an image that is:
- Virtual
- Erect
- Same size as the object
- At the same distance behind the mirror as the object is in front
- Laterally inverted
3. Spherical Mirrors
A spherical mirror has a reflecting surface that forms part of a sphere.
Types
Concave mirror
- Reflecting surface curves inward.
- It is a converging mirror for parallel rays.
Convex mirror
- Reflecting surface curves outward.
- It is a diverging mirror for parallel rays.
Important Terms
| Term | Meaning |
|---|---|
| Pole (P) | Centre of the reflecting surface |
| Centre of curvature (C) | Centre of the sphere of which the mirror is a part |
| Radius of curvature (R) | Distance (PC) |
| Principal axis | Straight line passing through P and C |
| Principal focus (F) | Point where parallel rays meet, or appear to meet, after reflection |
| Focal length (f) | Distance between P and F |
| Aperture | Effective diameter of the reflecting surface |
For a spherical mirror with a small aperture:
R=2f
Therefore, f=\frac R2
The focus lies midway between the pole and centre of curvature.
4. Image Formation by a Concave Mirror
The image depends strongly on the object’s position.
| Object position | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F | Highly diminished | Real, inverted |
| Beyond C | Between C and F | 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 obtained at a finite distance |
| Between F and P | Behind mirror | Enlarged | Virtual, erect |
Most important case to remember
Object between P and F → enlarged, virtual and erect image.
This is why a concave mirror can be used as a shaving mirror and by dentists for obtaining enlarged views.
5. Ray Rules for Spherical Mirrors
For ray diagrams, usually any two suitable rays are enough.
Rule 1 — Parallel ray
A ray parallel to the principal axis:
- Concave mirror → reflects through F.
- Convex mirror → appears to come from F.
Rule 2 — Focus ray
A ray passing through F:
- Concave mirror → reflects parallel to the principal axis.
- For a convex mirror, a ray directed towards F reflects parallel to the principal axis.
Rule 3 — Centre of curvature
A ray passing through C, or directed towards C in a convex mirror, is reflected back along its original path.
Rule 4 — Pole
A ray striking the pole obeys the ordinary law of reflection:
i=r
Exam tip: For a ray diagram, draw the principal axis first and use two standard rays. Their intersection gives the image position.
6. Uses of Concave Mirrors
Concave mirrors are used in:
- Torches
- Searchlights
- Vehicle headlights
- Shaving mirrors
- Dental mirrors
- Solar furnaces
Their applications depend on their ability to produce either parallel beams or enlarged images, depending on object position.
7. Convex Mirror
A convex mirror always produces an image that is:
- Virtual
- Erect
- Diminished
- Located behind the mirror between P and F for an ordinary finite object.
For an object at infinity, the image forms at F and is extremely small.
Why is a convex mirror used as a rear-view mirror?
Because it:
- Produces an erect image.
- Produces a diminished image.
- Provides a wide field of view, allowing the driver to see a larger region behind the vehicle.
8. New Cartesian Sign Convention — Mirrors
Take the pole P as origin and the principal axis as the x-axis.
Remember:
- Object is normally placed to the left.
- Distances measured to the right → positive.
- Distances measured to the left → negative.
- Heights above principal axis → positive.
- Heights below principal axis → negative.
Common signs
| Quantity | Concave mirror | Convex mirror |
|---|---|---|
| Focal length (f) | Negative | Positive |
| Radius (R) | Negative | Positive |
| Object distance (u) | Negative | Negative |
9. Mirror Formula
The relationship between object distance (u), image distance (v), and focal length (f) is:
frac1v+\frac1u=\frac1
It applies to spherical mirrors generally, provided the correct sign convention is used.
Also:
R=2f
10. Magnification — Mirror
Magnification tells how large the image is compared with the object.
m=\frac{h’}h
For spherical mirrors:
m=-\frac vu
where:
- (h) = object height
- (h’) = image height
- (u) = object distance
- (v) = image distance
A negative magnification indicates a real, inverted image, while a positive magnification indicates a virtual image under the convention used in the chapter.
PART B — REFRACTION OF LIGHT
11. Refraction
Refraction is the change in direction of light when it travels obliquely from one transparent medium to another.
Examples:
- A pencil partly immersed in water appears displaced.
- The bottom of a water tank appears raised.
- Objects viewed through glass may appear shifted.
The underlying reason is that the speed of light changes when it enters another medium.
12. Bending of Light
Rarer → Denser medium
Light slows down and bends towards the normal.
Denser → Rarer medium
Light speeds up and bends away from the normal.
Here, “optically denser” does not necessarily mean greater mass density. A medium with a larger refractive index is optically denser than one with a smaller refractive index.
Very important:
Towards normal → rarer to denser
Away from normal → denser to rarer
13. Refraction through a Rectangular Glass Slab
At the first surface:
Air → Glass
The ray bends towards the normal.
At the second surface:
Glass → Air
The ray bends away from the normal.
Because the two surfaces are parallel:
- The emergent ray becomes parallel to the incident ray.
- But it is shifted sideways from its original path.
Key point
Parallel in direction does not mean the ray follows exactly the same path.
There is a lateral shift.
14. Laws of Refraction — Snell’s Law
First law
The incident ray, refracted ray and normal at the point of incidence lie in the same plane.
Second law
For a particular pair of media and a given colour of light:
\frac{\sin i}{\sin r}=\text{constant}
This is called Snell’s law.
The constant is the refractive index of the second medium relative to the first.
15. Refractive Index
For light travelling from medium 1 to medium 2:
{n_{21}=\frac{v_1}{v_2}}
]
where:
- (v_1) = speed of light in medium 1
- (v_2) = speed of light in medium 2
For absolute refractive index:
[
\boxed{n=\frac cv}
]
where:
- (c) = speed of light in vacuum
- (v) = speed of light in the medium
The speed of light in vacuum is approximately:
3\times10^8\text{ m/s}
Meaning of refractive index
If a medium has a larger refractive index, light travels more slowly through it and it is optically denser relative to a medium with a lower refractive index.
PART C — SPHERICAL LENSES
16. What is a Lens?
A lens is a transparent material bounded by surfaces, with at least one surface being spherical.
Convex lens
- Thicker in the middle.
- Thinner at the edges.
- Converges light rays.
- Also called a converging lens.
Concave lens
- Thinner in the middle.
- Thicker at the edges.
- Diverges light rays.
- Also called a diverging lens.
17. Important Terms for Lenses
Optical centre (O)
Central point of the lens.
A ray passing through the optical centre travels approximately without deviation.
Principal axis
Straight line passing through the two centres of curvature.
Centres of curvature
A lens has two centres of curvature, usually denoted by (C_1) and (C_2).
Principal focus
A convex lens brings parallel rays to a point called its principal focus.
A concave lens makes parallel rays appear to diverge from its principal focus.
A lens has two principal foci, (F_1) and (F_2).
Focal length
f=\text{distance between optical centre and principal focus}
18. Image Formation by Convex Lens
| Object position | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F₂ | Highly diminished | 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 at finite distance |
| Between F₁ and O | Same side as object | Enlarged | Virtual, erect |
Most important case
Object between F and O → enlarged, virtual and erect image.
This is the principle behind using a convex lens as a magnifier.
19. Concave Lens — Image Formation
A concave lens always forms an image that is:
- Virtual
- Erect
- Diminished
- On the same side of the lens as the object
- Between the optical centre and principal focus for an ordinary object.
This remains true irrespective of the object’s position.
20. Ray Rules for Lenses
Ray 1 — Parallel ray
For a convex lens:
Parallel ray → passes through the principal focus on the opposite side.
For a concave lens:
Parallel ray → appears to come from the principal focus on the same side.
Ray 2 — Focus ray
For a convex lens:
Ray through focus → emerges parallel to principal axis.
Ray 3 — Optical centre
A ray through the optical centre travels without deviation.
Exam technique: For most lens ray diagrams, use any two standard rays and locate their intersection or apparent intersection.
21. Sign Convention — Lenses
The same general Cartesian convention is used, but distances are measured from the optical centre O.
Important:
\text{Convex lens: }f>0
\text{Concave lens: }f<0
Correct signs must be used for (u,v,f,h,h’).
22. Lens Formula
The relationship between object distance, image distance and focal length is:
\frac1v-\frac1u=\frac1f
This formula is applicable to spherical lenses when the proper sign convention is followed.
23. Magnification — Lens
m=\frac{h’}
Also:
m=\frac vu
where:
- (h) = object height
- (h’) = image height
- (u) = object distance
- (v) = image distance
Interpretation
- (m>1) → enlarged image
- (m<1) in magnitude → diminished image
- Negative (m) → inverted image
- Positive (m) → erect image
24. Power of a Lens
Power tells us how strongly a lens converges or diverges light.
P=\frac1f
Here (f) must be expressed in metres.
SI unit
Dioptre (D)
1D=1,m^{-1}
Sign
- Convex lens → positive power
- Concave lens → negative power
Quick examples
If:
P=+2D
then the lens is convex and
f=\frac1{2}=0.5m
If:
P=-2.5D
then the lens is concave and
f=-0.4m
25. Combination of Lenses
When lenses are placed in contact, their powers add algebraically:
P=P_1+P_2+P_3+\cdots
Example:
+2D+0.25D=+2.25D]
This principle is useful in optical instruments and corrective lens systems.
Formula
Mirrors
R=2f
frac1v+\frac1u=\frac1f
m=\frac{h’}h=-\frac vu]
Refraction
frac{\sin i}{\sin r}=n
n_{21}=\frac{v_1}{v_2}
n=\frac cv
Lenses
\frac1v-\frac1u=\frac1f
m=\frac{h’}h=\frac vu
P=\frac1f
1D=1m^{-1}
Comparison Table
| Feature | Concave mirror | Convex mirror | Convex lens | Concave lens |
|---|---|---|---|---|
| Action on parallel rays | Converges | Diverges | Converges | Diverges |
| Typical nature | Converging mirror | Diverging mirror | Converging lens | Diverging lens |
| Can form real image? | Yes | No | Yes | No |
| Can form virtual image? | Yes | Yes | Yes | Yes |
| Always erect? | No | Yes | No | Yes |
| Always diminished? | No | Yes | No | Yes |
Common Exam Traps
1. Optical density ≠ mass density
A medium being optically denser does not necessarily mean it has greater mass density.
2. Convex mirror vs convex lens
Both have “convex” in their names, but:
- Convex mirror → diverges reflected rays.
- Convex lens → converges refracted rays.
3. Concave mirror is not always magnifying
Its image depends on the object’s position.
4. Concave lens always gives
Virtual + erect + diminished image.
5. Convex mirror always gives
Virtual + erect + diminished image.
6. Sign conventions matter
Do not substitute distances as positive simply because they are measured lengths. Use the New Cartesian Sign Convention.
7. Power calculation
Always convert focal length into metres before using:
P=\frac1f
Last-Minute Revision
If you have only a few minutes, remember these points:
- Reflection: (i=r)
- Concave mirror: can form real or virtual images.
- Convex mirror: always virtual, erect and diminished.
- Mirror formula: (\frac1v+\frac1u=\frac1f)
- Mirror magnification: (m=-v/u)
- (R=2f)
- Refraction: change in direction due to change in speed.
- Rarer → denser: bends towards normal.
- Denser → rarer: bends away from normal.
- Snell’s law: (\sin i/\sin r=\text{constant})
- Refractive index: (n=c/v)
- Convex lens: converges light.
- Concave lens: diverges light.
- Concave lens: always virtual, erect and diminished.
- Lens formula: (\frac1v-\frac1u=\frac1f)
- Lens magnification: (m=v/u)
- Power: (P=1/f), with (f) in metres.
- Convex lens power: positive.
- Concave lens power: negative.
- Lenses in contact: (P_{\text{total}}=P_1+P_2+\cdots)