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: hi=ho ; di=do

• 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{concave} negative, f{convex} positive

Mirror Formula & Magnification

• \frac{1}{f}=\frac{1}{v}+\frac{1}{u}

• Magnification m=\frac{hi}{ho}= -\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{21}=\frac{v1}{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 F1, F2, R=2f

Image by Convex Lens

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

• Beyond 2F1 → between F2,2F_2, diminished, real-inverted

• At 2F1 → at 2F2, same size, real-inverted

• Between F1,2F1 → 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{convex}>0, f{concave}<0

Lens Formula & Magnification

• \frac{1}{f}=\frac{1}{v}-\frac{1}{u}

• Magnification m=\frac{hi}{ho}=\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{total}=\sum Pi

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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.

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.