Resolving Power of Telescope and Microscope

Q: Point out all the differences between Microscope and Telescope

Microscope Telescope This optical instrument is used to see very small objects like cells ,study of diseases This optical instrument is used to see very large object like Celestial body ,study of solar system The aperture of the object is small The aperture of the object is large In this , Eye piece is greater than focal length In this optical instrument focal length is greater than Eyepiece.

Resolving Power of Telescope and Microscope - A Complete Guide

Edited By Vishal kumar | Updated on Jul 02, 2025 04:47 PM IST

In this chapter, we will study about resolving power and learn more about resolving the power of Telescope and Microscope . We will study the resolving power of Grating, limit of resolution and resolving power of human Eye. In the last we will see the difference between telescope and microscope and study further in details about resolution limit, types of microscope and unit of numerical aperture.

JEE Main/NEET 2027: Physics Important Formulas for Class 10

NEET 2025: Mock Test Series | Syllabus | High Scoring Topics | PYQs

JEE Main: Study Materials | High Scoring Topics | Preparation Guide

JEE Main: Syllabus | Sample Papers | Mock Tests | PYQs

This Story also Contains

What is Resolving Power and Resolution in Physics
Difference between Telescope and microscope
Microscope
Telescope

Resolving Power of Telescope and Microscope - A Complete Guide

What is Resolving Power and Resolution in Physics

When two point size object placed at minimum separation either linear or angular for which they appears just separated is known as limit of Resolution of an optical instrument
The reciprocal of limit of resolution of an optical aperture is known as Resolving Power

Difference between resolution and magnification is that the former is distinct between two objects and later enlarges the objects.

The Rayleigh criterion for the minimum resolvable angle is

θmin = 1.22 λ/D

Where, D is the diameter of the aperture of the instrument

Also read -

NEET Highest Scoring Chapters & Topics

This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.

Download E-book

Resolving Power of Grating

It is the capacity of an aperture to separate two different diffraction maxima formed by two different wavelengths which are very close to each other.

Resolving Power and its SI unit

Resolving Power of optical instruments is defined as the capacity of its to distinguish between smaller details .

For the objects to be distinguished kept at a smaller distance , resolving power should be higher.

SI unit of Resolving Power

Resolving power is dimensionless quantity and thus it has no SI unit

Note: Resolving Power is the ratio between mean wavelength of different spectral lines and difference of wavelength between them and as there is the same quantity having the same unit thus there is no SI unit.

Difference between Telescope and microscope

A Telescope is an optical instrument which let us see object up close which is at distant from it like Planets , Stars etc. while
A microscope is an optical instrument which also allows seeing objects up close but with detailed magnification. This instrument is used mainly to enlarge and magnify smaller objects like microorganisms , cells, study of plants etc.

Related Topics Link,

Microscope

Resolving power of Microscope/Resolving power of microscope formula
The resolving power formula is given by:
Resolving power = 1/ Difference in Distance(∆d) =2a / λ
Where a is the numerical aperture and λ is the wavelength

Types of Microscope

Light Microscope
Compound microscope

Resolution of Electron Microscope

As we know Resolution depends upon wavelength and wavelength of electrons is much smaller than other particles so theoretically resolution of electron microscope comes to be unlimited.

Resolution of Compound Microscope

Restraints of resolution of simple Microscope can be removed by using Compound Microscope as it has two lens arrays namely objective lens and Eyepiece. The combination of these lens arrays results in formation of an enlarged virtual image.

Numerical Aperture Derivation

NA= √( Ƞ1^2- Ƞ2^2)

Where, Ƞ1 is refractive index of core

Ƞ2 is refractive index of cladding.

Also Read:

Telescope

Telescope is an optical instrument which consists of a lens , mirror or combination of both these to close up distant objects by means of absorption, reflection of electromagnetic radiation.

Types of telescope

On the basis of wavelength Telescope is distinguished as:

Optical Telescope

X-Ray Telescope

Ultraviolet Telescope

Telescope Resolution

It is an ability of a telescope to distinguish two point source objects into different images.

Principles of Telescope

We try to understand this by an example:

Let's say on a hazy night we were driving through the forest and were experiencing a lot of obstacles to see through the foggy light . We saw a beam of light coming towards us and we were unable to study the origin of point source or unable to distinguish the point source but as the object came closer by, we found it was a four wheeler instead of motorbike as we could easily see different point sources of light.

Same principle is followed by Telescope

Telescope Power

In simple term , Telescope power is its ability to enlarge its object size

Resolving power of Telescope formula is given by:

Resolving Power =D/d= a / 1.22 λ

Where D= distance of object from the lens of telescope

a= Resolution of two slit

How can we change Resolving Power

As we can see Resolving Power of a telescope depends on the resolution of two slits, so by increasing the value of (a) we can increase the power value.

Resolving Power of an Eye

Like telescopes or other optical instruments our Eyes also have resolving power. It depends on size of pupils ,as compared to diameter of aperture of other optical instruments our pupils size is comparatively very small hence it is obvious that resolving power of our Eyes is lower than all other optical instruments.

Also check-

NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. What is angular Resolution in an optical instrument?

From a distant ,we can’t able to judge the separation between the source point but as the object comes closer ,we can barely resolve and tell the difference between the two images .Hence angular resolution depends upon the distance (L)

L: distance of image from Eye. It is always in radian

2. Point out all the differences between Microscope and Telescope

Microscope	Telescope
This optical instrument is used to see very small objects like cells ,study of diseases	This optical instrument is used to see very large object like Celestial body ,study of solar system
The aperture of the object is small	The aperture of the object is large
In this , Eye piece is greater than focal length	In this optical instrument focal length is greater than Eyepiece.

3. Resolving power of a microscope is a function of ____

Wavelength of light and numerical aperture of the lens.

4. The resolving power of electron microscope is greater than that of an optical microscope. Why?

Because, the wavelength of visible light is greater than the wavelength of electrons.

5. What is the difference between angular resolution and spatial resolution?

Angular resolution refers to the ability to distinguish between two point sources separated by a small angle, typically used for telescopes observing distant objects. Spatial resolution refers to the ability to distinguish between two points separated by a small distance, often used in microscopy for nearby objects.

6. What is meant by "empty magnification" in microscopy?

Empty magnification occurs when the magnification of an image is increased beyond the point where additional useful detail can be resolved. It makes the image larger but doesn't reveal any new information, often resulting in a blurry or pixelated appearance.

7. What is meant by "diffraction-limited" resolution?

Diffraction-limited resolution refers to the best possible resolution an optical system can achieve, limited only by the diffraction of light. It represents the theoretical maximum resolving power of the instrument, assuming perfect design and no other limiting factors.

8. What is the Abbe diffraction limit?

The Abbe diffraction limit, formulated by Ernst Abbe, describes the fundamental maximum resolution of a microscope. It states that the smallest resolvable distance is approximately half the wavelength of the light used, divided by the numerical aperture of the objective lens.

9. What is the relationship between resolving power and the Airy disk?

The Airy disk is the central bright spot in the diffraction pattern of a point source. The size of the Airy disk is inversely related to resolving power: a smaller Airy disk indicates better resolving power. Two point sources are generally considered resolvable when their Airy disks are separated enough to be distinguished.

10. How does numerical aperture affect a microscope's resolving power?

A higher numerical aperture (NA) improves a microscope's resolving power. NA is a measure of the microscope objective's ability to gather light and resolve fine specimen detail. Higher NA values allow for better resolution of smaller details.

11. How does immersion oil improve a microscope's resolving power?

Immersion oil increases the refractive index between the objective lens and the specimen, allowing light rays that would otherwise be lost to total internal reflection to enter the objective. This increases the numerical aperture and thus improves resolving power.

12. What is super-resolution microscopy?

Super-resolution microscopy refers to various techniques that allow microscopes to resolve details smaller than the diffraction limit. These methods, such as STED or PALM, use clever illumination schemes or photoactivatable fluorophores to overcome the traditional resolution limit.

13. How does the resolving power of an electron microscope compare to a light microscope?

Electron microscopes generally have much higher resolving power than light microscopes. This is because electrons have a much shorter wavelength than visible light, allowing for resolution of much smaller structures, down to the atomic scale in some cases.

14. How does coherent light (like lasers) affect resolving power?

Coherent light sources like lasers can potentially improve resolving power by providing a more uniform and controlled illumination. However, they can also introduce interference effects that may complicate image interpretation.

15. Why do larger telescope apertures provide better resolving power?

Larger apertures collect more light and create a larger diffraction pattern. This allows for finer angular resolution, enabling the telescope to distinguish smaller details and more closely spaced objects in the night sky.

16. How does atmospheric turbulence affect a telescope's resolving power?

Atmospheric turbulence causes rapid variations in the refractive index of air, leading to distortions in the wavefront of light from celestial objects. This effectively limits the resolving power of ground-based telescopes, often well below their theoretical diffraction limit.

17. What is adaptive optics and how does it improve telescope resolving power?

Adaptive optics is a technology that corrects for atmospheric distortions in real-time. It uses deformable mirrors controlled by computers to counteract the effects of atmospheric turbulence, allowing ground-based telescopes to approach their theoretical diffraction-limited resolving power.

18. Can resolving power be improved indefinitely by increasing magnification?

No, increasing magnification alone does not improve resolving power indefinitely. There's a limit to useful magnification based on the instrument's resolving power. Beyond this, you get "empty magnification" where the image appears larger but no additional detail is revealed.

19. How does the resolving power of the human eye compare to optical instruments?

The human eye has a resolving power of about 1 arcminute under optimal conditions. This is much lower than most telescopes and microscopes, which is why these instruments allow us to see details invisible to the naked eye.

20. What is resolving power in optics?

Resolving power is the ability of an optical instrument, like a telescope or microscope, to distinguish between two closely spaced objects or points. It determines the level of detail an instrument can reveal in an image.

21. How does wavelength affect resolving power?

Shorter wavelengths of light generally provide better resolving power. This is because the diffraction limit, which determines the smallest resolvable detail, is proportional to the wavelength of light used.

22. What is the Rayleigh criterion?

The Rayleigh criterion is a common standard used to determine the theoretical resolving power of an optical instrument. It states that two point sources are considered just resolvable when the central maximum of one diffraction pattern coincides with the first minimum of the other.

23. What role does diffraction play in limiting resolving power?

Diffraction is the primary factor limiting resolving power in well-designed optical instruments. It causes light to spread out when passing through an aperture, creating a diffraction pattern that sets a fundamental limit on the smallest details that can be resolved.

24. What is the relationship between f-number and resolving power in a camera lens?

A lower f-number (larger aperture) generally provides better resolving power in a camera lens. This is because a larger aperture allows more light to enter and reduces the effects of diffraction, enabling the lens to resolve finer details.

25. How does pixel size in a digital camera sensor affect resolving power?

Smaller pixel sizes can potentially improve resolving power by allowing finer sampling of the image. However, there's a trade-off: very small pixels collect less light, potentially increasing noise. The optimal pixel size depends on the optical system's resolving power and the intended use of the images.

26. How does phase contrast microscopy affect resolving power?

Phase contrast microscopy doesn't directly improve resolving power, but it enhances the visibility of transparent specimens by converting phase shifts in light to amplitude changes. This can make previously invisible structures apparent, seemingly improving resolution, though the actual resolving power remains the same.

27. What is the role of aperture synthesis in radio telescope arrays?

Aperture synthesis allows multiple small radio telescopes to work together as if they were a single large telescope. This technique dramatically improves the resolving power of radio astronomy observations, allowing for much finer angular resolution than any single dish could achieve.

28. How does oil immersion affect the numerical aperture of a microscope objective?

Oil immersion increases the numerical aperture by reducing the refractive index mismatch between the objective lens and the specimen. This allows light rays at higher angles to enter the objective, increasing the NA and thereby improving the resolving power.

29. How does chromatic aberration affect resolving power?

Chromatic aberration occurs when different wavelengths of light are focused at different points, causing color fringing and reduced sharpness. This effectively reduces the resolving power of the optical system by blurring the image and making fine details harder to distinguish.

30. What is the significance of the Dawes limit in astronomy?

The Dawes limit is an empirical formula used to estimate the resolving power of telescopes for visual observation. It provides a practical estimate of the smallest angular separation between two stars that can be resolved, taking into account both the theoretical diffraction limit and human visual perception.

31. How does the concept of resolving power apply to spectroscopy?

In spectroscopy, resolving power refers to the ability to distinguish between closely spaced spectral lines. It's typically defined as the ratio of the wavelength to the smallest detectable wavelength difference. Higher resolving power allows for more detailed analysis of spectral features.

32. How does the shape of the aperture affect the diffraction pattern and resolving power?

The shape of the aperture influences the shape of the diffraction pattern. For example, a circular aperture produces an Airy disk pattern, while a rectangular slit produces a sinc function pattern. These differences can affect how closely spaced objects can be resolved in different directions.

33. What is the relationship between resolving power and the point spread function (PSF)?

The point spread function describes how a point source of light is spread out by an optical system. A narrower PSF indicates better resolving power, as it means the system can more accurately reproduce point sources without blurring them together.

34. How does image stacking improve apparent resolving power in astrophotography?

Image stacking involves combining multiple exposures of the same subject. While it doesn't improve the actual resolving power of the telescope, it can significantly improve the signal-to-noise ratio, making finer details more visible and creating an image that appears to have better resolution.

35. What is the difference between resolution and resolving power?

Resolution typically refers to the number of pixels in a digital image or the fineness of detail in a photograph. Resolving power, on the other hand, is the ability of an optical system to distinguish between separate points or objects. High resolution doesn't necessarily mean high resolving power, and vice versa.

36. How does the Nyquist sampling theorem relate to resolving power in digital imaging?

The Nyquist theorem states that to accurately represent a signal, it must be sampled at least twice the highest frequency present. In imaging, this means the pixel size should be at least half the size of the smallest detail you want to resolve. Sampling below this rate can lead to aliasing and loss of resolution.

37. What is meant by "diffraction-free" beams, and how do they relate to resolving power?

Diffraction-free beams, such as Bessel beams, maintain their transverse intensity profile as they propagate. While they don't truly overcome the diffraction limit, they can maintain a narrow focus over longer distances than conventional beams, potentially improving the effective resolving power in certain applications.

38. How does polarization affect resolving power?

Polarization itself doesn't directly affect resolving power, but techniques using polarized light can enhance contrast or enable super-resolution methods. For example, polarization can help distinguish between closely spaced features with different optical properties, effectively improving the ability to resolve structures.

39. What is the role of deconvolution in improving apparent resolving power?

Deconvolution is a computational technique that attempts to reverse the blurring effects of the point spread function. While it doesn't increase the actual resolving power of the optical system, it can significantly enhance the apparent sharpness and detail in images, making structures easier to distinguish.

40. How does the concept of resolving power apply to gravitational wave detectors?

In gravitational wave astronomy, resolving power relates to the ability to distinguish the directions of gravitational wave sources. Improved resolving power allows more precise localization of events, which is crucial for multi-messenger astronomy where gravitational wave detections are correlated with observations in other parts of the electromagnetic spectrum.

41. What is the relationship between coherence length and resolving power in interferometry?

Coherence length is the distance over which a wave maintains a predictable phase relationship. In interferometry, longer coherence lengths allow for the combination of light from more widely separated apertures, potentially improving the resolving power of the interferometer.

42. How does the Strehl ratio relate to resolving power?

The Strehl ratio is a measure of the quality of an optical system, comparing the peak intensity of the actual point spread function to that of an ideal, diffraction-limited system. A higher Strehl ratio indicates better optical quality and generally correlates with better resolving power.

43. What is meant by the "diffraction barrier" in microscopy?

The diffraction barrier refers to the fundamental limit on resolution imposed by the wave nature of light. It's typically about half the wavelength of the light used for imaging. Super-resolution techniques aim to overcome this barrier through various clever approaches.

44. How does the concept of resolving power apply to mass spectrometry?

In mass spectrometry, resolving power refers to the ability to distinguish between ions with slightly different mass-to-charge ratios. Higher resolving power allows for more precise mass measurements and the ability to separate and identify more closely related compounds.

45. What is the relationship between the f-number and the Airy disk size?

The size of the Airy disk is directly proportional to the f-number of the optical system. A smaller f-number (larger aperture) produces a smaller Airy disk, which generally corresponds to better resolving power.

46. How does spherical aberration affect resolving power?

Spherical aberration causes light rays passing through different parts of a lens to focus at slightly different points. This spreads out the focal point, effectively increasing the size of the Airy disk and reducing the resolving power of the system.

47. What is the significance of the Sparrow criterion in resolving power?

The Sparrow criterion is an alternative to the Rayleigh criterion for defining resolving power. It states that two point sources are considered resolved when the combined intensity distribution shows a flat top rather than a single peak. It's sometimes considered more realistic for actual detection scenarios.

48. How does the concept of resolving power apply to holography?

In holography, resolving power relates to the finest interference fringes that can be recorded and reconstructed. Higher resolving power in the recording medium allows for the capture and reproduction of finer details in the holographic image.

49. What is the relationship between resolving power and the modulation transfer function (MTF)?

The modulation transfer function describes how well an optical system preserves contrast at different spatial frequencies. A system with better resolving power will maintain higher contrast at higher spatial frequencies, resulting in a better MTF.

50. How does the concept of resolving power apply to radar systems?

In radar systems, resolving power typically refers to the ability to distinguish between closely spaced targets. It's often described in terms of range resolution (ability to distinguish targets at similar distances) and angular resolution (ability to distinguish targets at similar angles).

51. What is the role of pupil apodization in modifying resolving power?

Pupil apodization involves modifying the transmission or phase profile across the aperture of an optical system. While it typically reduces overall light throughput, it can reshape the point spread function, potentially improving resolving power for specific applications or suppressing certain artifacts.

52. How does the concept of resolving power apply to hearing and auditory perception?

In auditory perception, resolving power relates to the ability to distinguish between sounds of similar frequency. The cochlea acts as a frequency analyzer, with different regions responding to different frequencies. Better frequency resolution (higher resolving power) allows for finer discrimination of pitch and timbre.

53. What is the relationship between resolving power and the depth of field?

Depth of field and resolving power are often in tension. Optical systems with very high resolving power (like those with large apertures) tend to have a shallow depth of field. Conversely, increasing the depth of field (e.g., by using a smaller aperture) often reduces the system's ability to resolve fine details due to diffraction effects.

54. How does quantum entanglement potentially affect resolving power?

Quantum entanglement offers the potential for quantum-enhanced imaging techniques that can surpass classical resolution limits. For example, ghost imaging using entangled photons can potentially achieve better resolving power than classical techniques under certain conditions, though practical implementations remain challenging.