Summary and Quick Revision

Chapter at a Glance

Light – Reflection and Refraction — the essentials.

• Reflection: angle of incidence = angle of reflection; incident ray, normal, reflected ray in one plane.
• Spherical mirrors: concave (converging) and convex (diverging). Terms: P, C, R, F, f, principal axis, aperture. $R = 2f$.
• Refraction: light bends on changing medium because its speed changes. Rarer→denser bends towards the normal; denser→rarer bends away.
• Refractive index: $n = c/v$; higher n = optically denser = slower light.
• Lenses: convex (converging) and concave (diverging). Power $P = 1/f$ in dioptres.

Mirrors — Formulas and Images

• Mirror formula: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ (plus sign). $f = R/2$.
• Magnification: $m = \dfrac{h'}{h} = -\dfrac{v}{u}$.
• Sign convention: object on left ($u$ negative); concave $f$ negative, convex $f$ positive.

Mirror	Image
Concave, object beyond F	real, inverted (size varies with position)
Concave, object between P and F	virtual, erect, enlarged
Convex (any position)	virtual, erect, diminished

$m<0$ real/inverted; $m>0$ virtual/erect.

Refraction and Refractive Index

• Refraction bends light due to a change in speed. Along the normal ($i=0$): no bending.
• Glass slab: refracts twice; emergent ray parallel to incident ray, laterally shifted.
• Laws of refraction: (i) incident ray, refracted ray, normal in one plane; (ii) Snell's law $\dfrac{\sin i}{\sin r}$ = constant.
• Refractive index: $n_{21} = \dfrac{v_1}{v_2}$; absolute $n = \dfrac{c}{v}$ ($c = 3\times10^8$ m/s).
• Higher n = optically denser = slower light. Optical density ≠ mass density.

Lenses — Formulas and Power

• Lens formula: $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ (minus sign). Convex $f$ positive, concave $f$ negative.
• Magnification: $m = \dfrac{h'}{h} = \dfrac{v}{u}$ (no minus, unlike mirrors).
• Power: $P = \dfrac{1}{f}$ (f in metres); SI unit dioptre (D); convex +, concave -. Lenses in contact: $P = P_1 + P_2 + \ldots$

Lens	Image
Convex, object beyond F	real, inverted (size varies)
Convex, object between F and O	virtual, erect, enlarged (magnifier)
Concave (any position)	virtual, erect, diminished

Master One-Liners (Morning-of-Exam Revision)

1. Laws of reflection: $\angle i = \angle r$; rays and normal coplanar.
2. $R = 2f$; focus midway between P and C.
3. Concave = converging (real focus); convex = diverging (virtual focus).
4. Convex mirror & concave lens: always virtual, erect, diminished.
5. Concave mirror & convex lens give enlarged erect image only for object within F.
6. Mirror formula: $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$; mirror m $= -\frac{v}{u}$.
7. Lens formula: $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$; lens m $= \frac{v}{u}$.
8. $u$ always negative; concave $f$ negative, convex $f$ positive (mirror & lens).
9. Rarer→denser: towards normal; denser→rarer: away from normal.
10. Along the normal: no bending.
11. Glass slab: emergent ray parallel to incident ray (lateral shift).
12. Snell's law: $\frac{\sin i}{\sin r}$ = constant = refractive index.
13. $n = c/v$; higher n = optically denser = slower light.
14. Power $P = 1/f$ (metres); unit dioptre; convex +, concave -.
15. Lenses in contact: $P = P_1 + P_2 + \ldots$