Tag: optics diagram drawing

How to draw the ray diagram used to derive the distance between the virtual sources in the Bi-prism experiment?

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

1. Introduction:

       The Bi-prism experiment is a fascinating way to study interference in optics. One of its most important tasks is finding the distance between the two virtual sources, S₁ and S₂. We calculate this distance using the conjugate foci method.

       In this blog, you’ll learn how to draw the ray diagram for this method using simple and smart construction techniques. These steps follow the same rules explained in my earlier post, “How to Draw Diagrams in Physics Using Smarter Techniques.”

Let’s begin.

 2.  Understanding the bi-prism experiment: Conjugate foci method:

     2.1.  The conjugate foci method plays a vital role in measuring the distance (d) between two virtual sources in the Bi-prism experiment. To determine this distance, a lens of focal length f is placed between the bi-prism and the eyepiece, with the eyepiece located at a distance of 4f from the slit.

     The lens is then moved between two key positions:

 L₁: Lens close to the bi-prism

 L₂: Lens close to the screen

    In both positions, we observe different separations between the images of S₁ and S₂. These measurements help us calculate the true source separation.

     2.2.  Two key lens positions in the bi-prism experiment:

1. Position L₁ (Lens close to bi-prism):

    In this position, when the lens is closer to the Bi-prism (as shown in Fig. A), magnified images of the two virtual sources (S₁ and S₂) are formed.

    The distance d₁ between the magnified virtual sources is measured.

2. Position L₂ (Lens near screen):

    In the second position, when the lens is moved towards the screen (as shown in Fig. B), diminished images of S₁ and S₂ are observed.

    The distance d₂ between the diminished virtual sources is measured.

    3. Mathematical derivation for determining the distance between virtual        sources:

    In the bi-prism experiment, the object distance (u) and image distance (v) for the lens are related to the distances measured between the virtual sources.

 For position L₁ (Fig. A below):

       d₁/d = v/u

  where d₁ is the distance between magnified virtual sources.

 For Position L₂  (Fig. B below):

    d₂/d = u/v

  Where, d₂ is the distance between diminished virtual sources.

   By multiplying these two equations and rearranging them, we can find the distance d between the two virtual sources as

          d² = d₁. d₂

This is how the conjugate foci method is used to calculate the distance between S₁ and S₂.

4. Smarter Techniques for Drawing Ray Diagram:

Fig. A

     Fig. B

  4.1. Prepare the grid and principal axis:

   Step 1: Draw the frame:

•  On unruled A4, first draw one vertical reference line near the left margin.

   Step 2: From this line, draw 16 equally spaced light horizontal grid lines across the page; number them 1 to 16 in your mind for counting.

   Step 3: Fix the optical length:

• From the top reference line, mark a point so that the useful diagram height is about 12 cm.

   Step 4: Within this height, keep all important points (sources, lens, images) restricted to a central 2 cm vertical strip so the construction remains neat and symmetrical.

   Step 5: Choose the principal axis:

• Take the 6th horizontal grid line as the principal axis; mark it clearly.
• Count and note that the 13th line will be used for the eyepiece/screen side of the construction, matching the arrangement used in the biprism experiment. Mark the virtual sources S₁ and S_2. Mark coherent virtual sources

• On the left half of the principal axis region, choose a short central segment and draw two small ticks: two grid steps above the axis for S₁ and two grid steps below for S₂.
• Label them S₁ and S₂, and note that the vertical gap between them represents the virtual source separation d (same in both Fig A and Fig B).
•  Mark lens positions and image separations.

   Step 6: Draw lens positions L₁ and L₂ 

• For Fig A (lens nearer bi-prism), go to about the 4 cm mark from the source side and draw a vertical line crossing all grid lines; thicken the central part and shape it as a convex lens; this is position L₁.7.For Fig B (lens nearer screen), go to about the 8 cm mark from the source side and similarly draw another convex lens; this is position L_2.

 Step 7: Fix magnified separation d₁ in Fig A:

• In Fig A, from the principal axis on the eyepiece side, count 4 lines up and 4 lines down and put small points on the eyepiece line; label the upper point A₁ and the lower point B₁.
• The distance A₁ B₁ along the eyepiece line represents d₁, the magnified separation of the virtual sources when the lens is at L₁.8. Fix diminished separation d₂ in Fig B

   Step 8:  In Fig B, on the eyepiece side, go just one line above and one line below the axis and mark two points on the eyepiece line; label them A₂ (above) and B₂ (below).

• The distance A₂ B₂ now represents d₂, the diminished separation of virtual sources for lens position L₂.

  4.2. Construct rays for Fig A (lens near bi-prism):

 Step 1: Mark optical center and draw circular arcs

• In Fig A, choose a point on the axis inside the lens as the optical centre O.
• With a compass, take a convenient radius (about 6 cm on your grid) and from O draw two light circular arcs that pass through A₁ and B₁; extend these arcs back towards S₁ and S₂ to guide your ray directions.9.Join sources to images through the lens

• Draw straight lines S₁O and OB₁; also draw S₂O and OA₁. These show rays passing undeviated through the optical center.
• From A₁ and B₁, draw lines back to meet the lens boundary, and then from those points continue the incident parts of the rays towards S₁ or S₂, adding arrowheads to show the direction from sources to images.

   Step 2: Show incident, refracted rays and focus 

• For each pair, thicken the part of the ray before the lens as incident and the part after the lens as refracted, with arrows pointing towards the images A₁ and B₁.
• Extend two refracted rays (one from S₁, one from S₂) until they intersect on the axis behind the lens; mark this intersection as the focal point of the convex lens in position L₁, indicating that A₁ and B₁ are magnified real

4.3. Construct rays for Fig B (lens near screen):

 Step 1: Join images back to sources

• In Fig B, mark the optical center O of lens in position L₂.

 Step 2: Draw lines A₂O and OS₁, and B₂O and OS₂, representing rays passing through O; then from A2 and B2 construct incident and refracted parts exactly as done in Fig A but now giving diminished images on the eyepiece line. Complete parallel ray construction

• From the image side intersections on the lens surface, draw rays backward parallel to the principal axis to meet S₁ and S₂, adding arrows to show travel from S₁, S₂ through the lens to A₂, B₂.
• Extend suitable pairs of refracted rays to meet at the focal point on the other side of the lens, indicating that A₂ and B₂ are diminished real images when the lens is near the screen.

  4.4. Label formula and result on the sheet:

  Show conjugate foci relation:

• Beside Fig A, write d₁ / d = v / u; beside Fig B, write d₂ / d = u / v, indicating that u and v are interchanged in the two positions.
• Below both figures, write the final relation d = √(d₁ .d₂), stating that this gives the true separation d of the two virtual sources in the bi-prism experiment by conjugate foci method.

This completes the ray construction for the Bi-prism conjugate foci method.

  5. Conclusion:

   In this blog, we explored a clear and practical method for drawing the ray diagram used to calculate the distance between virtual sources in the Bi-prism experiment. By following these steps, you can easily construct neat and accurate diagrams that help you understand how object distance, image distance, and source separation relate to each other.

 6. Video support:

To learn the smarter drawing technique visually, watch the video below: