How to draw ray diagrams for a Convex Lens, Compound Microscope and Telescope? (Student-friendly guide)

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

1. Introduction:

     If ray diagrams feel confusing or “too neat to be real”, this guide is for you. This guide helps you draw scientifically accurate ray-diagrams for image formation by a convex lens, and further for a compound microscope and a simple astronomical telescope — using a “smart diagram” technique that is examination friendly, easy to draw, and visually clear.

   It walks you through each diagram step by step, with simple rules you can remember in examinations, and you can always pause and copy along with the video lesson.

 2. Key concepts and definitions:

Before drawing, know these basic terms:

2.1.  Principal Axis: 

  A straight horizontal line through the optical centre of a symmetrical lens.

2.2.  Optical Center (O):

   The midpoint of the lens (on the principal axis), through which a ray passes undeviated.

 2.3. Focus (F): 

  The point on the principal axis where rays parallel to the principal axis converge after passing through a convex (converging) lens.

 2.4. Twice the Focus (2F) (or  Center of curvature): 

  A point on the principal axis at twice the distance from the optical center as the focus; often used to locate object or image for standard cases.

 2.5. Real / Virtual Image:

• Real image: Where refracted rays actually converge; can be projected on a screen.
• Virtual image: Where refracted rays only appear to diverge from; cannot be projected, appears behind lens or eyepiece.

 2.6. Erect / Inverted Image:  

  Orientation of image arrow relative to object arrow (upright vs upside-down).

 3.Understanding these is essential before drawing:

   General “Smart Drawing” Tips (Use for All Diagrams):

 3.1.  Use roughly half an A4 page for a single diagram — large enough for clarity yet compact enough for examination notebooks.

3.2.  Draw with a pencil, sharpened at both ends (for neat lines), and use a full-size ruler (≈ 30 cm) for straight rays.

 3.3. First draw a clean principal axis — a horizontal line across the middle. Mark the optical centre (O) roughly at the center.

3.4.  Mark the focus (F) and twice focus (2F) points on both sides of the lens symmetrically.

 3.5. Draw the lens (just as a vertical line or simple double-concave/convex curve on the axis) — this keeps the diagram schematic and clear.

3.6.  Draw the object as an arrow (straight vertical line with arrow-head) perpendicular to the principal axis — on the left side (for standard lens problems).

4. Convex Lens:

4.1. Rules for ray diagram:

1.  Parallel ray to principal axis passes through focus on other side of convex lens.
2. Ray passing through Optical center of convex lens goes un-deviated.
3. Intersection of these rays gives position of Image.
4. Taking object on left side of lens, position of Image can be found.

4.2. Convex lens ray diagram for image due to object kept beyond 2F_1.

Goal: To locate the image formed by a convex lens when the object is placed beyond 2F.

Step 1: Draw line in the middle of half page.

Step 2:

1. Select a point 2F₁at 3 cm from margin. 
2. Draw a curve of length touching 3 lines above and below of middle line, having 6 cm radius and 2F₁as center.

Step 3:

1. Select a point 2F₂ on principal axis at 6 cm from one end of curve.
   2. Draw opposite curve of 6 cm radius from 2F₂.

Step 4:

     Select points F₁, F₂ on principal axis from O on both sides at a distance equal to half distance between O and 2F₁.

Step 5:

1. Draw 1 cm AB arrow headed perpendicular line to Principal axis near

     margin as object.

2. Draw parallel line to axis from B up to lens, make this line to pass from F₂.
3. Then draw line passing through O from B till it intersects line through F₂.
4. Draw perpendicular line A₁B₁ from intersection of above lines.

Step 6 :

  The final image due to convex lens, when object is kept beyond 2F₁ and image is formed between 2F₂ and F₂   and it is inverted, diminished, and real.

 

  4.3. Image due to object kept between F₁ and O:

Practice to draw image due to object kept between F₁ and O.

  4.4. Repeat same procedure to draw images due to object kept:
 1. at 2F₁
 2. Between   2F₁ and F₁
 3.  At  F₁  
 4. Between F₁ and O

Images due to Convex Lens:

  4.5. Summary table — Image formed by convex lens:

Object position	Image position	Image nature	Size
Beyond 2F	Between F and 2F	Real, Inverted	Smaller
At 2F	At 2F	Real, Inverted	Same
Between F and 2F	Beyond 2F	Real, Inverted	Magnified
At F	At infinity	Real	Highly enlarged
Between F and O	Same side	Virtual, Erect	Magnified

  5. Ray diagram for a Compound Microscope:

  A compound microscope uses two convex lenses — an objective (closer to object) and an eyepiece (closer to eye). The final image you see is virtual and highly magnified.

 5.1. To draw image due to Compound Microscope, follow the procedure used for convex lens:

Step 1:

 1. Compound microscope consists of objective and eye-piece.
 2.  Turn the full page to horizontal, draw line at   middle of horizontal page.
 3.   Draw objective of radius 6 cm.
 4.   Fix the points 2F_1O, F_1O, O, 2F_2O, F_2O.

  5. Draw object of 1 cm height between 2F_1O, F_1O and complete diagram

         for image A₁B₁ as per procedure .

Final image A₁B_1, due to objective of microscope, which is magnified, inverted, real.

Step 2:

Select point X at 3 cm from image A₁B_{1 .}

Step 3:

1. Draw Eye-piece with radius 8cm taking  1F_1Eat 8 cm from X.
   2. Fix points 2F_1E, F_1E, O, 2F_2E, F_2E.

Step 4 :

1 Draw final image A₂B₂ with eye-piece taking   A₁B₁ as object.
2 Final image is magnified, inverted, virtual.

  6. Ray diagram for a Simple Telescope (Astronomical Telescope):

   A basic telescope also uses two convex lenses

1. an objective (large focal length)
2. an eyepiece (short focal length) ,

arranged so that the final image is for a distant object (effectively at infinity).

 6.1. To draw image due to Telescope, follow the procedure used for convex lens.

Step 1:

1. Telescope consists of Objective and Eye-piece.
2. Turn the full page to horizontal, draw line at middle of horizontal page.
3. Draw objective of radius 8 cm. Fix the points 2F_1O, F_1O, O, 2F_2O, F_2O.

Step 2 :

1. Draw a line 1 passing through O with small inclination to horizontal.

      2 . Then draw parallel line 2 to this above up to lens.

3. Make this line 2 to pass through F_2Etill it intersects line 1 at B_1.
4. Draw first image A₁B₁due to objective between F_2E and 2 F_2E.

Step 3:

Fix point X at a distance of 2 cm from image A₁B_{1 .} 

Step 4:

1. Fix point 2F_1E at 6 cm from X.
2. Draw Eye-piece at X with radius 6 cm.
3. Fix points 2F_1E, F_1E, O, 2F_2E, F_2E.

Step 5:

1. Draw final image A₂B₂with eye-piece, taking image A₁B₁

      as object for eye-piece .

2. Final image is magnified, inverted, and virtual.

Thus using the given procedure ray diagrams can be easily drawn.

 7. Common mistakes to avoid:

  7.1.  Marking F and 2F asymmetric or too close/far — destroys accuracy.

 7.2. Drawing lens as thick or unrealistic, better to use a simple vertical line or gentle convex curve.

 7.3. Not using a straight ruler for rays → leads to messy/inaccurate diagrams.

 7.4. Drawing object-arrow too big or too small → distorts relative size of image.

7.5.  Forgetting to draw at least two rays from object — then image location will be ambiguous.

 8. Why This Method Works (and Helps in Examinations):

   8.1. The simplified but systematic approach avoids messy drawing and reduces errors.

  8.2.  Using standard notation (O, F, 2F) — students easily interpret and generalize for different cases.

  8.3.  Making diagrams on half-page makes them exam-friendly (fits within answer sheet, remains legible).

  8.4. The reuse of the same two-ray method for all object positions and optical devices helps memorize logically rather than by rote.

  9. Conclusion and final advice:

  Once you master the logic behind the principal axis, focus points, and ray-rules, you don’t need to memorize separately for every case. Instead, apply the same “draw-object → draw rays → locate image → label” method systematically

  With proper pencil technique, carefully marked F and 2F, and a good ruler — your diagrams will look clean, correct, and exam-ready.

10. Practice and perfection tips:

• Redraw each setup at least twice for hand memory.
• Use the same notation consistently (O, F, 2F, A, B, etc.).
• When revising, mentally visualize where the image forms for each case — this sharpens conceptual clarity.

Happy drawing — and best of luck mastering optics!

11. Video help:

   How to draw the ray diagram for images formed by convex lens, Microscope and Telescope — Motivational Physics.
https://youtu.be/d8qB-EhQ5Ik?si=aSI7E8Ku-gj9s2pr