Question

With the help of a diagram, show how a plane wave is reflected from a surface. Hence verify the law of reflection.

Answer 1

According to the laws of reflection:

• At the point of incidence, the incident rays, reflected rays, and normal to the reflecting surface all lie in the same plane.
• On opposing sides of the normal are the incident and reflected rays.
• The angle of incidence and the angle of reflection are the same. i.e., ∠i = ∠r.

Explanation:

                Reflection of light

XY: Plane reflecting surface

AB: Plane wavefront

RB₁: Reflecting wavefront

A₁M, B₁N: Normal to the plane

∠AA₁M = ∠BB₁N = ∠i = Angle of incidence

∠TA₁M = ∠QB₁N = ∠r = Angle of reflection

• A plane wavefront AB is advancing obliquely towards the plane reflecting surface XY. AA₁ and BB₁ are incident rays.
• When ‘A’ reaches XY at A₁, then the ray at ‘B’ reaches point 'P’ and it has to cover distance PB₁ to reach the reflecting surface XY.
• Let 't' be the time required to cover distance PB₁. During this time interval, secondary wavelets are emitted from A₁ and will spread over a hemisphere of radius A₁R, in the same medium. The distance covered by secondary wavelets to reach from A₁ to R in time t is the same as the distance covered by primary waves to reach from P to B₁. Thus A₁R = PB₁ = ct.
• All other rays between AA₁ and BB₁ will reach XY after A₁ and before B₁. Hence they will also emit secondary wavelets of decreasing radii.
• The surface touching all such hemispheres is RB₁ which is the reflected wavefront, bounded by reflected rays A₁R and B₁Q.
• Draw A₁M ⊥ XY and B₁N ⊥ XY.
  Thus, the angle of incidence is ∠AA₁M = ∠BB₁N = i and the angle of reflection is ∠MA₁R = ∠NB₁Q = r.
  ∠RA₁B₁ = 90 - r
  ∠PB₁A₁ = 90 - i
  In ΔA₁RB₁ and ΔA₁PB₁
  ∠A₁RB₁ = ∠A₁PB₁
  A₁R = PB₁ ....(Reflected waves travel an equal distance in the same medium in equal time.)
  A₁B₁ = A₁B₁ ....(Common side)
  ∴ ΔA₁RB₁ ≅ ΔA₁PB₁
  ∴ ∠RA₁B₁ = ∠PB₁A₁
  ∴ 90 - r = 90 - i
  ∴ i = r
• Also from the figure, it is clear that incident rays, reflected rays and normal lie in the same plane.
• This explains the laws of reflection of light from a plane reflecting surface on the basis of Huygens' wave theory.

Note:

1. Frequency, wavelength and speed of light do not change after reflection.
2. If reflection takes place from a denser medium, then the phase changes by π radians.