Chapter 9: Light — Reflection and Refraction
Light is a form of energy that enables us to see objects. It travels in a straight line and shows two important phenomena: reflection (bouncing back from a surface) and refraction (bending while passing from one medium to another).
Reflection of Light
When light falls on a highly polished surface (like a mirror), most of it bounces back. This is called reflection.
Laws of Reflection
- The angle of incidence (i) is equal to the angle of reflection (r). i.e. ∠i = ∠r
- The incident ray, the reflected ray, and the normal (drawn at the point of incidence) all lie in the same plane.
These laws are valid for all reflecting surfaces, including curved (spherical) mirrors.
Spherical Mirrors
A spherical mirror is a part of a hollow sphere whose one surface is reflecting.
- Concave mirror: reflecting surface curves inward (bulges away from the source). It is a converging mirror.
- Convex mirror: reflecting surface bulges outward. It is a diverging mirror.
Important Terms
- Pole (P): the centre of the reflecting surface of the mirror.
- Centre of curvature (C): centre of the sphere of which the mirror is a part.
- Radius of curvature (R): radius of that sphere (distance PC).
- Principal axis: straight line passing through the pole and the centre of curvature.
- Principal focus (F): point on the principal axis where rays parallel to the axis meet (concave) or appear to diverge from (convex) after reflection.
- Focal length (f): distance between the pole and the principal focus (PF).
Image Formation by Spherical Mirrors — Ray Rules
To locate an image, use any two of these rays:
- A ray parallel to the principal axis passes through F (concave) or appears to come from F (convex) after reflection.
- A ray passing through F (concave) or directed towards F (convex) becomes parallel to the principal axis after reflection.
- A ray passing through the centre of curvature C retraces its path (falls back along the same line) because it strikes the mirror normally.
- A ray incident obliquely at the pole is reflected making equal angles with the principal axis.
Images formed by a Concave Mirror
| Position of object | Position of image | Size | Nature |
|---|---|---|---|
| At infinity | At F | Highly diminished (point) | 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 | Highly enlarged | Real, inverted |
| Between P and F | Behind mirror | Enlarged | Virtual, erect |
Images formed by a Convex Mirror
A convex mirror always forms a virtual, erect and diminished image, located between the pole and focus behind the mirror — for objects at any distance.
Uses of Spherical Mirrors
- Concave: shaving mirrors, dentists' mirrors, torches/headlights/searchlights (reflectors), solar furnaces.
- Convex: rear-view (wing) mirrors in vehicles (wider field of view), on blind turns/roads.
Sign Convention (New Cartesian)
- The pole (P) is the origin; the principal axis is the x-axis.
- Distances are measured from the pole.
- Distances measured in the direction of incident light are positive; opposite to incident light are negative.
- Heights measured upward (above axis) are positive; downward are negative.
- So object distance u is always negative; focal length of a concave mirror is negative, of a convex mirror is positive.
Mirror Formula and Magnification
where v = image distance, u = object distance, f = focal length.
where h′ = height of image, h = height of object. If m is negative → real, inverted image; if positive → virtual, erect image. |m| > 1 means enlarged, |m| < 1 means diminished.
Refraction of Light
The bending of light as it passes obliquely from one transparent medium to another (due to change in speed) is called refraction.
- Going from a rarer to a denser medium (e.g. air → glass), light bends towards the normal.
- Going from a denser to a rarer medium (e.g. glass → air), light bends away from the normal.
Laws of Refraction
- The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
- Snell's law: the ratio of the sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media.
Refractive Index
The refractive index tells how much light slows/bends in a medium.
A medium with higher refractive index is optically denser. Diamond has the highest refractive index (about 2.42).
Refraction through a Rectangular Glass Slab
The emergent ray is parallel to the incident ray but is laterally displaced. The bending at the first surface (air→glass) is cancelled by opposite bending at the second surface (glass→air). The sideways shift is called lateral displacement.
Refraction by Spherical Lenses
- Convex (converging) lens: thicker in the middle; converges parallel rays to a real focus.
- Concave (diverging) lens: thinner in the middle; diverges parallel rays which appear to come from a virtual focus.
A lens has two principal foci and an optical centre (O). A ray through the optical centre passes undeviated. The distance 2F is at twice the focal length.
Ray Rules for Lenses
- A ray parallel to the principal axis passes through F (convex) or appears to come from F (concave) after refraction.
- A ray through the principal focus emerges parallel to the principal axis.
- A ray through the optical centre passes straight without deviation.
Images formed by a 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 | Highly enlarged | Real, inverted |
| Between F1 and O | Same side as object | Enlarged | Virtual, erect |
A concave lens always forms a virtual, erect and diminished image between the focus and optical centre, for objects at any distance.
Lens Formula, Magnification and Power
For lenses, a positive m means virtual & erect image; negative m means real & inverted image.
Power of a Lens
Power measures the degree of convergence or divergence of light rays a lens produces.
1 dioptre = power of a lens of focal length 1 metre. Power of a convex lens is positive; power of a concave lens is negative.