Light and Optics Revision Notes

Reflection of Light

Reflection occurs when a wave hits a surface and changes direction. Key terms include:

  • Normal: A perpendicular line to the reflecting surface.
  • Angle of Incidence: The angle between the incident ray and the normal.
  • Angle of Reflection: The angle between the reflected ray and the normal.

The angle of incidence equals the angle of reflection.

Examiners may provide the angle between the incident ray and the surface (not the normal) to trick students.

Image Formation by Reflection

When light from an object reflects off a mirror and reaches our eyes, our brain perceives the light as coming from behind the mirror, creating a virtual image.

Properties of the image in a flat mirror:

  • Same size as the object.
  • Same distance from the mirror as the object.
  • Virtual (cannot be seen on a screen).
  • Laterally inverted (left and right are reversed).

Ray Diagrams for Reflection

To find the position of a reflected image, follow these steps:

  1. Draw two light rays from the object hitting the mirror at different angles.
  2. Draw the normal at each point of incidence.
  3. Measure and draw the reflected rays, ensuring the angle of incidence equals the angle of reflection.
  4. Extend the reflected rays backward; their intersection point indicates the image location.

Refraction of Light

Refraction is the change in speed of a wave when it enters a different medium. If a wave hits a surface at an angle, it bends.
Light travels at approximately 3 × 10^8 m/s in air. When it enters a denser medium like glass, it slows down to approximately 2 × 10^8 m/s. Upon exiting the glass back into the air, it returns to 3 × 10^8 m/s.

  • Light hitting a surface at 90° does not bend.
  • When light travels from air to glass, it bends toward the normal.
  • When light travels from glass to air, it bends away from the normal.

Refractive Index

The refractive index (n) is the ratio of the speed of light in air to the speed of light in a medium. It can be calculated as: n = \frac{speed : of : light : in : air}{speed : of : light : in : medium}. It is also expressed using angles: n = \frac{sin : angle : in : air}{sin : angle : in : medium}.

Snell's Law relates the angles of incidence and refraction to the refractive index.

Critical Angle and Total Internal Reflection

When light travels from a denser medium (e.g., glass) to a less dense medium (e.g., air), several scenarios can occur:

  • Angle of Incidence < Critical Angle: Regular refraction occurs.
  • Angle of Incidence = Critical Angle: The refracted ray travels along the surface (90° to the normal).
  • Angle of Incidence > Critical Angle: Total internal reflection occurs; the light reflects back into the denser medium.

The critical angle (C) can be calculated using: n = \frac{1}{sin : C}

Total internal reflection requires:

  1. Light traveling from a more dense to a less dense medium.
  2. The angle of incidence being greater than the critical angle.

Optical Fibers

Optical fibres transmit light using total internal reflection. Light rays reflect inside the fiber because their angle of incidence is greater than the critical angle.

Applications:

  • Communication (internet broadband) for transmitting data.
  • Medicine (endoscopes) for seeing inside the body.

Dispersion of Light

Monochromatic light (single frequency) refracts without splitting.

White light, however, consists of multiple colors (red, orange, yellow, green, blue, indigo, violet). When white light refracts, it splits into these colors because each color has a different frequency and wavelength. This splitting is called dispersion.

Red bends the least (largest wavelength, lowest frequency), and violet bends the most (smallest wavelength, highest frequency).

Lenses

Convex (Converging) Lenses: Thick in the middle, thin at the edges. Parallel light rays converge at the focal point.

Concave (Diverging) Lenses: Thin in the middle, thick at the edges. Parallel light rays diverge as if coming from a focal point.

Focal Length: The distance between the center of the lens and the focal point.

Ray Diagrams for Lenses

To draw a ray diagram for a convex lens:

  1. Draw a horizontal ray from the top of the object to the center of the lens, then continue the ray through the focal point on the other side.
  2. Draw a ray from the top of the object straight through the center of the lens (no bending).
  3. (Optional) Draw a ray from the top of the object through the focal point on the same side of the lens, then continue the ray horizontally on the other side.

The intersection of these rays indicates the location of the image.

Image Properties:

  • Real Image: Light rays intersect; can be seen on a screen; inverted.
  • Virtual Image: Extensions of light rays intersect; cannot be seen on a screen; upright.

Image Size and Position with Convex Lenses

  • Object close to the lens (but beyond F): Image is real, inverted, enlarged, and farther away.
  • Object far from the lens: Image is real, inverted, diminished, and closer.
  • Object between the lens and F: Image is virtual, upright, and magnified.

Correcting Eyesight with Lenses

  • Shortsightedness: The eye focuses light in front of the retina. Corrected with a diverging lens to focus light on the retina.
  • Long-sightedness: The eye focuses light behind the retina. Corrected with a converging lens to focus light on the retina.