Light: Reflection & Refraction - Rapid Revision Notes

Light

Rectilinear Propagation of Light: Light travels in a straight line.
Speed of Light: Denoted as $c$ , approximately $3 \times 10^8$ m/s.

Reflection

Definition: The bouncing back of light from a shiny surface (e.g., mirror or water).
Laws of Reflection:
- The incident ray, the reflected ray, and the normal all lie in the same plane.
- Angle of incidence $\angle i$ = Angle of reflection $\angle r$

Mirrors

Plane Mirror:
- Smooth, polished surface with minimal bumps.
- Image Characteristics:
  - Always virtual and erect.
  - Image size equals object size.
  - Image distance behind the mirror equals object distance in front.
  - Laterally inverted.
Spherical Mirror: A mirror whose reflecting surface is part of a hollow sphere of glass.
- Concave Mirror: Reflecting surface is curved inwards.
- Convex Mirror: Reflecting surface is curved outwards.

Spherical Mirrors: Key Terms

Pole (P): The center of the reflecting surface.
Center of Curvature (C): The center of the sphere of which the mirror is a part.
Radius of Curvature (R): The radius of the sphere of which the mirror is a part.
Principal Axis: The straight line through the pole and center of curvature.
Principal Focus (F): The point where parallel rays converge (concave) or appear to diverge from (convex) after reflection.
Focal Length (f): Distance between the pole and the principal focus.
Aperture: Diameter of the reflecting surface.
Relationship between R and f for Concave Mirror: $R = 2f$
Relationship between R and f for Convex Mirror: $R = 2f$

Ray Diagrams: Rules

A ray parallel to the principal axis will pass through the focus after reflection.
A ray passing through the principal focus will become parallel to the principal axis after reflection.
A ray passing through the center of curvature will retrace its path after reflection.
A ray incident at the pole is reflected back making the same angle with the principal axis.

Concave and Convex Mirrors: Image Formation

Concave Mirror:
- Object at infinity: Image at focus, highly diminished, real and inverted.
- Object beyond C: Image between F and C, diminished, real and inverted.
- Object at C: Image at C, same size, real and inverted.
- Object between F and C: Image beyond C, enlarged, real and inverted.
- Object at F: Image at infinity, highly enlarged, real and inverted.
- Object between P and F: Image behind the mirror, enlarged, virtual and erect.
Convex Mirror:
- Object at infinity: Image at focus, highly diminished, virtual and erect.
- Object at any other position: Image between P and F, diminished, virtual and erect.

Uses of Concave and Convex Mirrors

Concave Mirrors:
- Torches, searchlights, vehicle headlights.
- Shaving mirrors.
- Dentist's mirrors.
- Solar furnaces.
Convex Mirrors:
- Rear-view mirrors in vehicles (preferred because they provide erect, diminished images and have a wider field of view).

Important Formulas and Sign Convention

Object Placement: Object typically to the left of the mirror.
Distance Measurement: Measured from the pole of the mirror.
Coordinate System:
- Positive x-axis: Right of origin.
- Negative x-axis: Left of origin.
- Positive y-axis: Above principal axis.
- Negative y-axis: Below principal axis.
Image Height (h’):
- Positive: Virtual images.
- Negative: Real images.
Magnification (m):
- Negative: Real images.
- Positive: Virtual images.
Mirror Formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ , where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance.
Magnification Formula: $m = \frac{h'}{h} = -\frac{v}{u}$ , where $h'$ is the image height and $h$ is the object height.

Problem-Solving Steps for Mirrors

Identify Given Values: Determine what the question is asking and the given values of $u$ , $v$ , and $f$ . Typically, two of these will be provided.
Apply Mirror Formula: Use the mirror formula to find the unknown value.
Magnification Analysis:
- m > 0: Image is upright.
- m < 0: Image is inverted.
- Concave Mirror:
- $f$ = always -ve
  - u = always -ve
  - v = -ve (real)
  - = +ve (virtual)

Convex Mirror
- f = always +ve
- u = always −ve
- v = always +ve (virtual)

Deduce Nature of Image: From the sign of $f$ , identify the type of mirror. From the sign of $v$ , determine the nature of the image formed by a concave mirror.
Apply Magnification Formula: If magnification is required, use the magnification formula. The value of $m$ indicates the nature of the image, and allows calculation of $h$ and $h'$ .
- h = +ve
- h′ = +ve (upright, virtual)
- = −ve (inverted, real)
- h = +ve
- h′ = +ve (virtual and upright)
Additional Insights from Magnification: The value of 'm' also provides insight into the type of mirror.

Refraction of Light

Definition: The change in direction of light as it passes from one transparent medium to another.
Laws of Refraction:
- The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
- Snell's Law of Refraction: States the relationship between the angles of incidence and refraction and the refractive indices of the two media.
Refractive Index: Measurement of how much a light ray bends when it passes from one medium to another.

Lenses

Definition: A transparent material bound by two surfaces, at least one of which is spherical.
Types:
- Convex Lens: Thicker in the middle (converging lens).
- Concave Lens: Thicker at the edges (diverging lens).

Lenses: Key Terms

Centre of Curvature (C, C1, C2): The center of the sphere from which the lens surface is a part.
Principal Axis: An imaginary straight line passing through the two centers of curvature.
Optical Centre (O): The central point of a lens where a ray of light passes without deviation.
Aperture: The effective diameter of the circular outline of a spherical lens.
Principal Focus (F, F1, F2): The point where rays parallel to the principal axis converge (convex) or appear to diverge from (concave).
Focal Length (f): The distance between the principal focus and the optical centre of a lens.

Ray Diagrams: Rules for Lenses

A ray of light from the object, parallel to the principal axis, after refraction through a convex lens, passes through the principal focus on the other side of the lens, or appears to diverge from the principal focus in case of a concave lens.
A ray of light passing through a principal focus, after refraction through a convex lens, will emerge parallel to the principal axis. A ray of light directed towards the principal focus, after refraction through a concave lens, will emerge parallel to the principal axis.
A ray of light passing through the optical centre of a lens will emerge without any deviation.

Convex Lens: Image Formation

Object at infinity: Image at F2, highly diminished, real and inverted.
Object beyond 2F1: Image between F2 and 2F2, diminished, real and inverted.
Object at 2F1: Image at 2F2, same size, real and inverted.
Object between F1 and 2F1: Image beyond 2F2, enlarged, real and inverted.
Object at F1: Image at infinity, highly enlarged, real and inverted.
Object between O and F1: Image on the same side as the object, enlarged, virtual and erect.

Concave Lens Image Formation

Object at infinity: Image at F1, highly diminished, virtual and erect.
Object at any other position: Image between F1 and O, diminished, virtual and erect.

Uses of Convex & Concave Lenses

Convex Lenses:
- Overhead projectors
- Cameras
- Focusing sunlight
- Simple telescopes
- Projectors
- Microscopes
- Magnifying glasses
Concave Lenses:
- Spyholes in doors
- Eyeglasses
- Some telescopes

Important Formulas for Lenses

All measurements are taken from the optical centre of the lens.
Focal length of a convex lens = positive.
Focal length of a concave lens = negative.
Lens Formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Magnification: $m = \frac{h'}{h} = \frac{v}{u}$
Power of Lens: $P = \frac{1}{f}$ , where $f$ is in meters. SI unit is Dioptre (D).
- 1 Dioptre is the power of a lens whose focal length is 1 meter.
- $1D = 1m^{-1}$
- Power of a convex lens = positive.
- Power of a concave lens = negative.

Problem-Solving Steps for Lenses

Identify Given Values: Determine what the question is asking and the given values of $u$ , $v$ , and $f$ . Typically, two of these will be provided.
Apply Lens Formula: Use the lens formula to find the unknown value.
- (m > 0): image is upright.
- (m < 0): The image is inverted
Deduce Nature of Image: From the sign of $f$ , identify the type of lens. From the sign of $v$ , determine the nature of the image formed by a convex lens.
- Concave Convex
  - f = always +ve
  - u = always −ve
  - v = +ve (real image)
  - = −ve(virtual image)
  - f = always −ve
  - u = always −ve
  - v = always −ve
Apply Magnification Formula: If magnification is required, use the magnification formula. The value of $m$ indicates the nature of the image, and allows calculation of $h$ and $h'$ .
Power of a lens asked then formula and sign conventions used:
- P (convex lens) = positive
- P (concave lens) = negative.
- f = always +ve
- f = always −ve

Additional Types of Questions

Screen-Based Questions: Problems involving slide projectors. The position of the screen needed for the slide projector to remain in focus.
Refractive Index and Speed of Light Questions: Refractive indexes of a particular medium and the speed of light in the medium; determine the speed of light in another medium.
Formula Used: $n = \frac{c}{v}$ , where $n$ is the refractive index, $c$ is the speed of light in vacuum, and $v$ is the speed of light in the medium.