Module 4.3 – Light: Reflection, Refraction & Lenses

Luminous object: emits its own light.
Refractive index $n$ : ratio of light speed in vacuum to that in the medium $(n = \frac{c}{v})$ .
Total internal reflection (TIR): complete reflection of light back into a medium when it strikes the boundary above the critical angle.
Concave lens (diverging): thinner at centre, spreads parallel rays outward.
Convex lens (converging): thicker at centre, brings parallel rays to a focus.

Reflection: $\angle i = \angle r$ (incident = reflection).
Snell’s law: $n1\sin\theta1 = n2\sin\theta2$ .
Light bends toward the normal when entering a higher $n$ ; away when entering a lower $n$ .

Image properties: upright, laterally inverted, same size, virtual, distance behind mirror equals object distance.
Lateral inversion: left–right reversal of image.
Smooth surfaces give regular reflection → sharp images.

Critical angle $\thetac$ : $\sin\thetac = \frac{n2}{n1}$ for n1 > n2.
No TIR when light travels into a medium of higher $n$ (cannot bend past $90°$ ).
Apparent depth: objects in water appear closer due to refraction toward the normal.
Underwater vision blurs because cornea–water have similar $n$ ; goggles restore air–cornea interface.

Focus (F): point where parallel rays meet/appear to meet after lens.
Convex lens:
• Distant object ⇒ real, inverted, diminished image at focus.
• Can also give virtual, upright, magnified image when object inside focal length.
Concave lens: always gives virtual, upright, diminished image.
Real images can be projected on a screen; virtual cannot.

v \text{(diamond)} < v \text{(glass)} < v \text{(Perspex)} < v \text{(ice)} < v \text{(water)} < v \text{(air)} (inverse of $n$ ).

Refraction makes a submerged pencil appear ‘broken’ at the water surface.
Coin-in-cup reappearance demonstrates refraction.
Increasing object–lens distance shifts image position (for convex lens, image moves toward focus).

Luminous object: emits its own light.
Refractive index $n$ : ratio of light speed in vacuum to that in the medium $(n = \frac{c}{v})$ .
Total internal reflection (TIR): complete reflection of light back into a medium when it strikes the boundary above the critical angle.
Concave lens (diverging): thinner at centre, spreads parallel rays outward.
Convex lens (converging): thicker at centre, brings parallel rays to a focus.

Reflection: $\angle i = \angle r$ (incident = reflection).
Snell’s law: $n1\sin\theta1 = n2\sin\theta2$ .
Light bends toward the normal when entering a higher $n$ ; away when entering a lower $n$ .

Image properties: upright, laterally inverted, same size, virtual, distance behind mirror equals object distance.
Lateral inversion: left–right reversal of image.
Smooth surfaces give regular reflection \u2192 sharp images.

Critical angle $\theta c$ : $\sin\theta c = \frac{n2}{n1}$ for n1 > n2.
No TIR when light travels into a medium of higher $n$ (cannot bend past $90°$ ).
Apparent depth: objects in water appear closer due to light refracting away from the normal as it passes from water (higher $n$ ) to air (lower $n$ ) before reaching the eye.
Underwater vision blurs because cornea–water have similar $n$ ; goggles restore air–cornea interface, allowing the eye's lens system to focus light properly.

Occurs only when light moves from high $n$ to low $n$ and \theta i > \theta c.
Enables optical fibres (light signals are guided along the fibre by continuous TIR), prisms (used in binoculars and periscopes to deviate light by $90°$ or $180°$ through TIR), sparkling of diamonds (designed to maximize internal reflections).

Focus (F): point where parallel rays meet/appear to meet after lens.
Convex lens:
\u2022 Distant object \u21d2 real, inverted, diminished image at focus.
\u2022 Can also give virtual, upright, magnified image when object inside focal length.
Concave lens: always gives virtual, upright, diminished image.
Real images can be projected on a screen; virtual cannot.

v\text{(diamond)} < v\text{(glass)} < v\text{(water)} < v\text{(air)}