Ray Optics and Optical Instruments — Class XII Physics Notes | eduPhysics
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Class XII · Chapter 09

Ray Optics and Optical Instruments

How mirrors and lenses bend and focus light predictably enough to build a camera, a microscope, and your own eye — treating light as simple straight-line rays.

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1Reflection by Spherical Mirrors

This chapter uses ray optics — treating light as straight lines, ignoring its wave nature (that comes back in the next chapter). A single, consistent sign convention makes every mirror and lens problem solvable with the same two formulas.

Mirror Formula
1/v + 1/u = 1/f, where f = R/2
u = object distance, v = image distance, f = focal length, R = radius of curvature. By convention, distances measured against the incident light's direction are negative.
Magnification
m = −v/u = h′/h
Negative m means an inverted image; |m| > 1 means magnified, |m| < 1 means diminished.

2Refraction and Snell's Law

Light bends when it crosses a boundary between media of different optical density, because its speed changes while its frequency stays fixed.

Snell's Law
n₁ sin θ₁ = n₂ sin θ₂
Refractive index n = c/v, where v is the speed of light in that medium. A ray bends toward the normal when entering a denser medium, and away from the normal when entering a rarer one.

3Total Internal Reflection

Going from a denser to a rarer medium, the refracted ray bends further from the normal as the angle of incidence increases. Past a certain angle — the critical angle — the refracted ray would need to bend more than 90°, which is impossible; instead, all the light reflects back into the denser medium.

Critical Angle
sin θc = 1/n
n = refractive index of the denser medium relative to the rarer one. This is the working principle behind optical fibres, the sparkle of a cut diamond, and mirages on a hot road.

4Refraction at a Spherical Surface

Single Spherical Surface
n₂/v − n₁/u = (n₂ − n₁)/R
This is the building block for lenses — a thin lens is just two such refracting surfaces in quick succession.

5Thin Lenses

Thin Lens Formula
1/v − 1/u = 1/f
Note the sign difference from the mirror formula — a common source of errors when switching between the two.
Magnification
m = v/u

6Lens Maker's Formula

Applying the spherical-surface refraction equation twice — once at each face of the lens — gives a formula for focal length purely in terms of the lens's shape and material:

Lens Maker's Formula
1/f = (n21 − 1)(1/R₁ − 1/R₂)
n21 = refractive index of the lens material relative to the surrounding medium, R₁ and R₂ = radii of curvature of the two faces. This is literally how opticians design a lens to hit a target focal length.

7Power of a Lens and Combination of Lenses

Power
P = 1/f (f in metres, P in dioptres, D)
A converging lens has positive power, a diverging lens negative — this is exactly the number printed on a spectacle prescription.
Lenses in Contact
1/F = 1/f₁ + 1/f₂ + ..., so P = P₁ + P₂ + ...
Powers simply add — the reason combining lenses is described in dioptres rather than focal lengths in most practical (and prescription) contexts.

8Refraction Through a Prism

A ray passing through a prism bends twice — once at each face — and the total deviation depends on the angle of incidence, reaching a minimum value at one specific angle.

Prism Formula (at minimum deviation)
n = sin[(A + Dm)/2] / sin(A/2)
A = prism's apex angle, Dm = angle of minimum deviation. This is a standard method for measuring a material's refractive index experimentally.

9Dispersion of Light

Refractive index depends slightly on wavelength — violet light bends more than red. A prism therefore splits white light into its constituent colours (VIBGYOR), spread out by angle since each wavelength deviates by a different amount.

10Natural Phenomena: Rainbow and Scattering

  • Rainbow: sunlight refracts, internally reflects once, and refracts again inside countless raindrops, dispersing into its spectrum — each droplet sends one colour to your eye depending on the exact angle.
  • Why the sky is blue: shorter (blue) wavelengths scatter far more strongly off air molecules than longer (red) wavelengths, filling the daytime sky with scattered blue light.
  • Why sunsets are red: at sunset, sunlight travels through much more atmosphere; most blue light scatters away before reaching you, leaving the redder wavelengths dominant.

11The Human Eye

The eye's lens adjusts its focal length (accommodation) to focus objects at different distances onto the retina. The near point (closest comfortable focus) is conventionally taken as 25 cm; the far point of a normal eye is at infinity.

  • Myopia (near-sightedness): distant objects focus in front of the retina; corrected with a diverging (concave) lens.
  • Hypermetropia (far-sightedness): near objects focus behind the retina; corrected with a converging (convex) lens.
  • Presbyopia: age-related loss of accommodation ability, often needing bifocal lenses.
  • Astigmatism: uneven corneal curvature, corrected with a cylindrical lens.

12Microscopes

Simple Microscope (Magnifying Glass), Image at Near Point
m = 1 + D/f
D = near point distance (25 cm). Using a shorter focal length lens gives higher magnification.
Compound Microscope
m = mo × me
Total magnification is the product of the objective lens's magnification and the eyepiece's (acting as a simple magnifier on the objective's real image) — this is how you get far higher magnification than a single lens could achieve alone.

13Telescopes

Astronomical Telescope (Image at Infinity)
m = fo / fe, tube length L = fo + fe
fo, fe = focal lengths of the objective and eyepiece. Unlike a microscope (which needs a short objective focal length for close objects), a telescope wants a long objective focal length — distant objects are effectively at infinity either way, so what matters is gathering more light and magnifying the resulting angle.

Formula Summary

Mirror Formula
1/v + 1/u = 1/f
Mirror Magnification
m = −v/u
Snell's Law
n₁sinθ₁ = n₂sinθ₂
Critical Angle
sinθ_c = 1/n
Lens Formula
1/v − 1/u = 1/f
Lens Maker's Formula
1/f = (n₂₁−1)(1/R₁−1/R₂)
Power
P = 1/f
Lens Combination
P = P₁+P₂+...
Prism Formula
n = sin[(A+D_m)/2]/sin(A/2)
Simple Microscope
m = 1+D/f
Telescope Magnification
m = f_o/f_e

Solved Examples

Example 1 · Concave Mirror

An object is placed 30 cm in front of a concave mirror of focal length 10 cm. Find the image position and magnification.

Solution: u = −30 cm, f = −10 cm. Using 1/v = 1/f − 1/u = −1/10 − (−1/30) = −3/30 + 1/30 = −2/30, so v = −15 cm.

m = −v/u = −(−15)/(−30) = −0.5. The image is real, inverted, and half the object's size, forming 15 cm in front of the mirror.

Example 2 · Convex Lens

A convex lens of focal length 20 cm forms an image of an object placed 30 cm from the lens. Find the image position and magnification.

Solution: u = −30 cm, f = +20 cm. Using 1/v = 1/f + 1/u = 1/20 − 1/30 = (3−2)/60 = 1/60, so v = +60 cm.

m = v/u = 60/(−30) = −2. The image is real, inverted, twice the object's size, formed 60 cm on the far side of the lens.

Quick Check

1. When used as a magnifying glass, a convex lens forms an image that is:
Real, inverted, magnified
✓ Virtual, erect, magnified (correct)
Real, erect, diminished
Virtual, inverted, diminished
2. Total internal reflection can occur only when light travels:
From rarer to denser medium
✓ From denser to rarer medium, beyond the critical angle (correct)
Through a vacuum
At normal incidence
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Electromagnetic Waves

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Wave Optics

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