Light – Reflection, Refraction & Lenses (Quick Review)

Light Basics

• Light: form of energy enabling vision; travels in straight lines (rectilinear propagation)

• Speed in vacuum $3\times10^{8}\ \text{m s}^{-1}$; decreases in denser media

Reflection of Light

• Reflection: bouncing back of light from a surface

• Laws: 1) $i=r$ 2) Incident ray, reflected ray, normal lie in same plane

• Lateral inversion: left–right reversal in plane-mirror images

Plane Mirror Image

• Image: virtual, erect, laterally inverted

• Size and distance: $h<em>i=h</em>o$ ; $d<em>i=d</em>o$

• Focal length $f=\infty$

Spherical Mirrors

• Concave: converging; Convex: diverging

• Key terms: Pole $P$, Centre $C$, Radius $R$, Focus $F$, $R=2f$

Image by Concave Mirror (object → image)

• At $\infty$ → at $F$, highly diminished, 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 $F$ → $\infty$ (no image)

• Between $P$ and $F$ → behind mirror, enlarged, virtual-erect

Image by Convex Mirror

• At $\infty$ → at $F$ (behind mirror), point-sized, virtual-erect

• Anywhere else → between $P$ and $F$, diminished, virtual-erect

Uses

• Concave: shaving/dentist mirrors, headlights, solar furnaces

• Convex: vehicle rear-view, security mirrors

Sign Convention (Mirrors)

• Distances measured from $P$ along incident light $+$, opposite $-$

• Height above axis $+$, below $-$

• For mirrors: $u$ negative, $f<em>{concave}$ negative, $f</em>{convex}$ positive

Mirror Formula & Magnification

• $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

• Magnification $m=\frac{h<em>i}{h</em>o}= -\frac{v}{u}$
  • $m>0$ virtual-erect; $m<0$ real-inverted

Refraction of Light

• Refraction: bending due to change in speed across media

• Laws (Snell): 1) Incident, refracted ray & normal coplanar 2) $\frac{\sin i}{\sin r}=n_{21}=\text{constant}$

• Rarer→denser: bends towards normal; denser→rarer: away

Refractive Index

• Absolute: $n=\frac{c}{v}$

• Relative: $n<em>{21}=\frac{v</em>1}{v_2}$

• Optically denser medium has higher $n$ (lower speed)

Glass Slab

• Emergent ray parallel to incident; lateral displacement produced

Lenses

• Convex (converging), Concave (diverging)

• Terms: Optical centre $O$, principal axis, foci $F<em>1, F</em>2$, $R=2f$

Image by Convex Lens

• $\infty$ → at $F_2$, point, real-inverted

• Beyond $2F<em>1$ → between $F</em>2,2F_2$, diminished, real-inverted

• At $2F<em>1$ → at $2F</em>2$, same size, real-inverted

• Between $F<em>1,2F</em>1$ → beyond $2F_2$, enlarged, real-inverted

• At $F_1$ → $\infty$ (no image)

• Between $O,F_1$ → same side, enlarged, virtual-erect

Image by Concave Lens

• All positions → between $O$ and $F$ on same side, diminished, virtual-erect

Uses

• Convex: magnifiers, hypermetropia glasses, microscope/telescope lenses

• Concave: myopia glasses, peepholes, beam expanders

Sign Convention (Lenses)

• Distance from $O$ along incident light $+$, opposite $-$

• $f<em>{convex}>0$, $f</em>{concave}<0$

Lens Formula & Magnification

• $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

• Magnification $m=\frac{h<em>i}{h</em>o}=\frac{v}{u}$
  • $m>1$ enlarged, $0<m<1$ diminished, $m<0$ real-inverted

Power of Lens

• $P=\frac{1}{f(m)}$ (in dioptre $D$ where $f$ in metres)

• Convex: $P>0$; Concave: $P<0$

• Combination: $P<em>{total}=\sum P</em>i$

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I apologize, but I am unable to generate diagrams or visual representations within this text-based format. I can only provide information in written text, including formulas and markdown formatting.

I apologize, but I am unable to generate diagrams or visual representations within this text-based format. I can only provide information in written text, including formulas and markdown formatting.