How to Draw the Ray Diagram for Refraction at a Plane Boundary Using Huygens’ Principle – Smarter Techniques

How to Draw the Ray Diagram for Refraction at a Plane Boundary Using Huygens’ Principle – Smarter Techniques

Author:
Prof. Kali C. S.
M.Sc., M.Ed., D.C.S.
50+ Years of Experience in Physics Teaching

1.Introduction:

      Accurate ray diagrams are essential for understanding optics, especially for students of Class 10 to 12. Many students try to copy the diagrams mechanically, but the real beauty of Physics lies in understanding how a diagram emerges from fundamental principles.

       In my earlier blog, How to Draw Diagrams in Physics – Smarter Techniques, I explained a set of general guidelines for drawing neat and conceptually strong diagrams on an A4 sheet.
In this post, let us use the same guidelines to understand how to draw the ray diagram for refraction at a plane boundary using Huygens’ Principle.

  2.Laws of refraction:

    When light travels from air into glass, it bends at the surface separating the two media. This bending is called refraction and is described by Snell’s law, which relates the angles of incidence and refraction to the speeds of light in the two media. Using Huygens’ Principle, this behaviour can be shown with a clear, step-by-step ray diagram that students can easily reproduce in examinations.

 This bending is governed by: 

    2.1. . Refraction happens when light enters a medium with a different speed.

   2.2. . First law of refraction:

Snell’s law: n=sin i /sin r=v₁/v₂

Where

• i = angle of incidence
• r = angle of refraction
• n = refractive index of the second medium with respect to the first
• v₁ = velocity in rarer medium
• v₂ = velocity in denser medium 

    2.3. Second law of refraction:

  The incident ray, refracted ray and the normal to the boundary all lie in the same plane.

These laws explain what happens—but Huygens’ Principle explains why it happens.

   3. Huygens’ principle in simple words:

         “Every point on a wavefront acts as a secondary source and sends secondary wavelets in all directions.”

   Using this idea, we can construct a wavefront in the refracted medium and from that, obtain the refracted ray.

    Huygens’ Principle not only explains refraction—it gives us a practical method to draw the ray diagram much more accurately.

   4. Why does refraction occur? (Wavefront explanation):

  When light enters a denser or rarer medium:

• The speed of light changes.
• Therefore, the secondary wavelets in the second medium grow at a different speed.
• As a result, the wavefront tilts.
• A ray drawn perpendicular to this new wavefront becomes the refracted ray.

     This is the core idea behind drawing the diagram.

   5. Smarter technique: step-by-step method to draw the ray diagram:

   Use an A4 sheet and follow the neat-diagram rules explained in the earlier blog.
         Then, draw the refraction diagram using these steps:

  5.1. Draw the boundary and normal

     Draw a horizontal line XY to represent the boundary between air (top) and glass (bottom).
  At point A on XY, draw a vertical line AM; this is the normal to the surface where the ray will meet     the boundary.

  5.2. Draw the incident rays from a distant source

• Place the ruler at point A so that its left edge passes through A and is slightly inclined (about 30°) to the XY line, with about 5 cm of the ruler above XY.
• Now draw two parallel lines along the edges of the ruler up to the XY line. Label the point where the right-side line meets the XY line as C.

   5.3. Mark the angle of incidence at A

• • At A, mark the angle between the incident ray PA and the normal AM as ∠i.
  • Indicate this angle clearly with a small arc and the symbol i.

  5.4. Show an incident wavefront and its secondary source

• Draw perpendicular to the line QC from A, mark a point B at foot of the perpendicular on QC.
• Line segment AB indicates the part of the incident wavefront that has already reached the mirror at A, while the point near B is still in the incident medium.
• When point A touches the boundary first, it starts sending secondary wavelets into the glass, while point B continues to advance in air toward the boundary.

  5.5. Mark distances in equal time
       Choose a small time interval t.

• In time t, point B moves in air to C on the boundary, a distance v₁t
• In the same time t, the secondary wavelet from A travels into glass a distance v₂t
• From A, draw an arc inside the glass with radius v₂t

  5.6. Draw the new refracted wavefront
      Join point C on the boundary to a point D on the arc so that CD just touches (is tangent to) the       arc from A.
      Line CD is the new refracted wavefront in the glass.

  5.7. Draw the refracted ray and identify angles
      From A, draw a line AR perpendicular to the refracted wavefront CD; this is the refracted ray in      glass.
   The angle between AR and the normal is the angle of refraction r.

  5.8. Connect the construction to Snell’s law
      In the geometry of triangle ACD:

• AC corresponds to distance v₁t in air.

• AD corresponds to distance v₂t in glass.
  From the similar triangles formed, the ratio of the sines of the angles equals the ratio of these distances, giving
  : n = sini/sinr = v₁/v₂

  5.9. Conclusion:

   Why this diagram is a “Smarter Technique”
     This construction lets students see both the ray and the wavefront picture in one diagram. It also      proves Snell’s law directly, instead of just stating it, and encourages neat, exam ready diagrams     that can be drawn accurately on an A4 sheet.

   6. Video support:

   Do you want to know “How to draw the Ray Diagram for Reflection at a plane      surface based on Huygens’ Principle?” using given guide lines?

  Let us see from following video for actual smarter method of drawing diagram.