Ray Optics

Topics covered: Reflection, refraction, plane and spherical mirrors, total internal reflection, prisms, lenses and combinations (JEE Main focus).

1) Nature of Light & Basic Concepts

• Light is an electromagnetic wave and does not require a medium.
• Speed of light in vacuum: c = 3 × 10⁸ m s⁻¹
• Colour of light depends on frequency, not wavelength.
• Persistence of vision = 0.1 s
• Resolving limit of human eye ≈ 1 minute of arc

Optical path length:

L = μd

Principle of reversibility:

If a ray of light is reversed, it retraces its original path.

2) Reflection

Laws of reflection:

• Incident ray, reflected ray and normal lie in the same plane.
• Angle of incidence = angle of reflection.

Plane Mirror

• Image is virtual, erect and same size as object.
• Image distance = object distance.
• Lateral inversion occurs.
• Minimum mirror height to see full image = half of person’s height.

Number of images (two mirrors inclined at angle θ):

If (360/θ) = m (integer):
n = m − 1 (general case)

3) Spherical Mirrors

Focal length:

f = R / 2

Mirror formula:

1/v + 1/u = 1/f

Magnification:

m = −v/u

Newton’s formula:

x₁x₂ = f²

• Concave mirror → converging
• Convex mirror → diverging

4) Refraction

Snell’s Law:

μ₁ sin i = μ₂ sin r

• Rarer → denser: ray bends towards normal
• Denser → rarer: ray bends away from normal

Apparent Depth

μ = Real depth / Apparent depth

Lateral displacement (small angle):

y = t(μ − 1)/μ

5) Total Internal Reflection (TIR)

Critical angle:

sin θ_c = 1/μ

• Occurs only when light travels from denser to rarer medium.
• At i > θ_c, entire light is reflected back.

6) Prism

Angle of deviation:

δ = i₁ + i₂ − A

Minimum deviation:

μ = sin[(A + δ_m)/2] / sin(A/2)

7) Refraction at Spherical Surface

Formula:

(μ₂/v) − (μ₁/u) = (μ₂ − μ₁)/R

Lateral magnification:

m = (μ₁ v) / (μ₂ u)

8) Lenses

Lens maker’s formula:

1/f = (μ − 1)(1/R₁ − 1/R₂)

Lens formula:

1/v − 1/u = 1/f

Magnification:

m = v/u

Power of lens:

P = 1/f (f in metres)

9) Combination of Lenses

Lenses in contact:

1/F = 1/f₁ + 1/f₂

Total power:

P = P₁ + P₂

Displacement method (convex lens):

Object size = √(I₁ × I₂)