IP Physics Notes (Upper Secondary, Year 3-4): 7) Light

Quick recap -- Light travels in straight lines until a boundary bends or reflects it. Track incident and refracted angles carefully and use lens rules to predict image position, size, and orientation.

Reflection Basics

• Reflection: bouncing of light from a surface.
• Law 1: incident ray, reflected ray, and normal all lie in the same plane.
• Law 2: angle of incidence equals angle of reflection, \( i = r \).
• Smooth surfaces give specular reflection; rough surfaces scatter light, producing diffuse reflection.
• Always draw the normal at the point of incidence before marking angles.

Plane Mirror Images

• Properties: virtual, upright, same size, laterally inverted, same distance behind the mirror as the object is in front.
• To construct paths: draw the apparent ray from image to eye first (dashed behind the mirror), then reflect it to locate the real ray into the eye.

Refraction & Refractive Index

• Refraction: change in direction when light crosses media because its speed changes.
• Snell's law: \[ n_1 \sin i = n_2 \sin r \]
• Refractive index definition: \( n = \dfrac{c}{v} \) (ratio of light speed in vacuum to medium).
• An alternative form (light entering from air): \( n = \dfrac{\sin i}{\sin r} \).
• Rays bend toward the normal when entering a higher index medium (slowing down) and away when exiting to lower index (speeding up).

Apparent Depth & Lateral Shift

• Objects under water appear shallower because emerging rays bend away; use similar triangles or Snell's law to quantify.
• Glass slabs cause lateral displacement of rays while keeping them parallel.

Total Internal Reflection (TIR)

• Occurs when light travels from a higher to a lower refractive index medium and the incidence angle exceeds the critical angle \( c \).
• Critical angle condition: \( \sin c = \dfrac{n_2}{n_1} \) (with \( n_1 > n_2 \)).
• Above \( c \), refraction cannot satisfy Snell's law, so all light reflects internally.
• Uses: optical fibres, prisms in periscopes, data transmission with minimal loss.

Worked Example: Optical Fibre Core

An optical fibre has core index \( n = 1.48 \) and cladding index \( 1.40 \). The critical angle at the core-cladding boundary is \[ \sin c = \frac{1.40}{1.48} \Rightarrow c = \sin^{-1}\left( \frac{1.40}{1.48} \right) \approx 72.1^\circ. \] Any ray meeting the boundary above \( 72.1^\circ \) (measured from the normal) undergoes TIR and stays in the core.

Thin Lenses

• Converging (convex) lens: brings parallel rays to a focus; can form real or virtual images.
• Diverging (concave) lens: spreads parallel rays; forms virtual, upright, diminished images.
• Focal length \( f \): distance from optical centre to focus. Sign convention: positive for converging, negative for diverging lenses.
• Lens equation (real-is-positive convention): \[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]
  • \( u \): object distance (positive when object sits in front of lens).
  • \( v \): image distance (positive for real images on the far side; negative for virtual images on the object side).
• Linear magnification: \[ m = \frac{v}{u} = \frac{\text{image height}}{\text{object height}} \]
  • \( \lvert m \rvert > 1 \) -> magnified, \( \lvert m \rvert < 1 \) -> diminished; negative magnification indicates image inversion.

Ray Construction Rules (Converging Lens)

1. Ray through the optical centre passes undeviated.
2. Ray parallel to principal axis refracts through the focus on the far side.
3. Ray through the near focus emerges parallel to the axis.

Image Cases for Converging Lenses

Worked Example: Lens Imaging

An object sits ( \pu{18 cm} ) in front of a converging lens with \( f = \pu{12 cm} \). Find the image distance and magnification. \[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \Rightarrow \frac{1}{12} = \frac{1}{18} + \frac{1}{v} \Rightarrow \frac{1}{v} = \frac{1}{12} - \frac{1}{18} = \frac{1}{36}. \] So \( v = \pu{36 cm} \) (real image). Magnification \( m = \frac{v}{u} = \frac{36}{18} = 2 \) -> image is inverted and twice the object height.

Diverging Lens Notes

• Use the same ray rules but treat focus positions as virtual (draw them on object side).
• The lens equation still applies with negative \( f \) and \( v \) for the virtual image.

Key Takeaways

• Always mark normals and apply Snell's law or reflection laws precisely.
• Critical-angle reasoning explains when light traps within a medium.
• Lens calculations combine algebra (lens/magnification equations) with ray diagrams for sign and orientation checks.
• Real vs virtual, magnified vs diminished outcomes stem from object position relative to \( f \) and \( 2f \).