Reflection & Refraction of Light

You see your reflection in a mirror every morning. You notice a pencil appearing bent in a glass of water. These phenomena -- reflection and refraction -- are fundamental to understanding how light behaves when it encounters different surfaces and media.

Laws of Reflection

1. The angle of incidence equals the angle of reflection: i = r
2. The incident ray, reflected ray, and normal all lie in the same plane

Mirror Formula

For spherical mirrors (concave and convex):

1/f = 1/v + 1/u

where f = focal length, v = image distance, u = object distance.

Sign convention (New Cartesian): Distances measured in the direction of incident light are positive. The pole is the origin.

Magnification: m = -v/u (negative for real/inverted, positive for virtual/erect)

Refraction and Snell's Law

When light passes from one medium to another, it changes speed and bends. This is refraction.

Snell's Law: n1 sin i = n2 sin r

where n1 and n2 are refractive indices of the two media.

The refractive index n = speed of light in vacuum / speed of light in medium.

Total Internal Reflection (TIR)

When light travels from a denser to a rarer medium, and the angle of incidence exceeds the critical angle (C), all light is reflected back. This is TIR.

sin C = n2/n1 (where n1 > n2)

Applications: Optical fibres, diamond sparkle, mirages on hot roads.

Lens Formula

For thin lenses (convex and concave):

1/f = 1/v - 1/u

Power of a lens: P = 1/f (in dioptres, D, when f is in metres)

Worked Example

An object is placed 30 cm from a convex lens of focal length 20 cm. Find the image position and magnification.

Solution:

• Using 1/f = 1/v - 1/u
• u = -30 cm (object on left), f = +20 cm
• 1/20 = 1/v - 1/(-30) = 1/v + 1/30
• 1/v = 1/20 - 1/30 = (3-2)/60 = 1/60
• v = +60 cm (real image, on the other side)
• m = v/u = 60/(-30) = -2 (inverted, magnified)

Nepal Connection

Optical fibres that bring internet connectivity to remote parts of Nepal rely on total internal reflection. The Sagarmatha region sometimes experiences mirages due to temperature gradients in the atmosphere -- a direct result of refraction.

Key Takeaways

• Mirror formula: 1/f = 1/v + 1/u; Lens formula: 1/f = 1/v - 1/u
• Snell's law relates angles and refractive indices during refraction
• TIR occurs when light goes from denser to rarer medium beyond the critical angle
• Sign conventions are crucial for correct calculations