Microscope vs. Telescope: A Detailed Comparison for JEE
Master the key differences in ray diagrams, magnifying power formulas, and adjustments for normal vs. relaxed vision.
Why This Comparison Matters for JEE
Microscopes and telescopes are frequently asked together in JEE to test your understanding of optical instruments. Students often confuse their working principles, formulas, and adjustments.
🎯 JEE Exam Pattern
Expect 1-2 questions from optical instruments in every JEE paper. Mastering this comparison can secure 4-8 easy marks and help you avoid common pitfalls.
🚀 Quick Navigation
1. Fundamental Differences
Purpose and Function
| Parameter | Microscope | Telescope |
|---|---|---|
| Purpose | Viewing very small nearby objects | Viewing distant objects |
| Object Distance | Just beyond focal length of objective | At infinity |
| Final Image | At distinct vision (25 cm) or infinity | At infinity or distinct vision |
| Focal Lengths | $f_o$ small, $f_e$ small | $f_o$ large, $f_e$ small |
| Aperture | Small | Large |
💡 Memory Aid
"Micro" = Small objects, Small focal lengths
"Tele" = Distant objects, Large objective focal length
2. Ray Diagrams Comparison
Compound Microscope
Ray Diagram (Normal Adjustment)
Key Points:
- Object placed just beyond $f_o$ of objective
- Objective forms real, inverted, magnified image
- This image acts as object for eyepiece
- Eyepiece acts as simple microscope
- Final image at infinity (normal adjustment)
Astronomical Telescope
Ray Diagram (Normal Adjustment)
Key Points:
- Distant object at infinity
- Objective forms real image at its focal plane
- This image acts as object for eyepiece
- Eyepiece placed so final image at infinity
- $f_o$ + $f_e$ = length of telescope
3. Magnifying Power Formulas
Compound Microscope Formulas
When final image at infinity:
Where:
$v_o$ = image distance from objective
$u_o$ = object distance from objective
$D$ = least distance of distinct vision (25 cm)
$f_e$ = focal length of eyepiece
When final image at D:
Approximately:
$$M \approx \frac{L}{f_o} \times \frac{D}{f_e}$$
Where $L$ = tube length
Astronomical Telescope Formulas
When final image at infinity (Normal Adjustment):
Where:
$f_o$ = focal length of objective
$f_e$ = focal length of eyepiece
Length of telescope = $f_o + f_e$
When final image at D:
Length of telescope:
$$L = f_o + u_e$$
Where $u_e$ = object distance for eyepiece
🎯 JEE Formula Strategy
- Microscope: Remember both cases (infinity and D)
- Telescope: $M = \frac{f_o}{f_e}$ for normal adjustment is most important
- Sign Convention: All measurements are positive for optical instruments
- Approximations: Often $u_o \approx f_o$ for microscope calculations
4. Adjustments for Different Vision Conditions
Normal vs. Relaxed Vision
| Condition | Microscope | Telescope |
|---|---|---|
| Normal Adjustment (Final image at infinity) |
• Eyepiece adjusted so final image at infinity • Less strain on eyes • $M = \frac{v_o}{u_o} \times \frac{D}{f_e}$ |
• Final image at infinity • $f_o + f_e$ = tube length • $M = \frac{f_o}{f_e}$ |
| Relaxed Vision (Final image at D = 25 cm) |
• Final image at least distance of distinct vision • Higher magnification • $M = \frac{v_o}{u_o} \left(1 + \frac{D}{f_e}\right)$ |
• Final image at D = 25 cm • Tube length increases • $M = \frac{f_o}{f_e} \left(1 + \frac{f_e}{D}\right)$ |
Microscope Adjustment Steps
- Place object just beyond $f_o$ of objective
- Adjust objective to get real, magnified image
- For normal vision: Adjust eyepiece so final image at infinity
- For maximum magnification: Adjust eyepiece so final image at D
- Use rack and pinion for fine adjustments
Telescope Adjustment Steps
- Point telescope towards distant object
- Adjust objective to get real image at its focal plane
- For normal vision: Place eyepiece so final image at infinity
- For maximum magnification: Adjust eyepiece so final image at D
- Use focusing knob for sharp image
⚠️ Common JEE Mistakes to Avoid
Mistake 1: Confusing Magnifying Power Formulas
Using telescope formula for microscope or vice versa. Remember: Microscope deals with small nearby objects, Telescope with distant objects.
Mistake 2: Wrong Sign Convention
Applying Cartesian sign convention to optical instruments. In optical instruments, all distances are taken as positive.
Mistake 3: Confusing Adjustments
Mixing up normal and relaxed vision conditions. Remember: Normal = image at infinity, Relaxed = image at D (25 cm).
📋 Quick Revision Sheet
Microscope Key Points
- For viewing small nearby objects
- $f_o$ and $f_e$ both small
- Object just beyond $f_o$
- Normal: $M = \frac{v_o}{u_o} \times \frac{D}{f_e}$
- Relaxed: $M = \frac{v_o}{u_o} \left(1 + \frac{D}{f_e}\right)$
Telescope Key Points
- For viewing distant objects
- $f_o$ large, $f_e$ small
- Object at infinity
- Normal: $M = \frac{f_o}{f_e}$, $L = f_o + f_e$
- Relaxed: $M = \frac{f_o}{f_e} \left(1 + \frac{f_e}{D}\right)$
🎯 Exam Tips
- Always specify which adjustment you're considering
- Draw quick ray diagrams for better understanding
- Remember D = 25 cm for least distance of distinct vision
- Practice numericals with both adjustment conditions
🎯 Practice Problems
Problem 1: A compound microscope has objective and eyepiece of focal lengths 2 cm and 5 cm respectively. The tube length is 20 cm. Calculate magnifying power when final image is at infinity.
Problem 2: An astronomical telescope has objective of focal length 100 cm and eyepiece of focal length 5 cm. Calculate length of telescope and magnifying power in normal adjustment.
Problem 3: Compare the magnifying power of a microscope when final image is at infinity vs at D = 25 cm.
Ready to Master More Ray Optics?
Continue your JEE Physics preparation with our comprehensive optical instruments module