arXiv abstract link

arXiv abstract link

**Telescope and Microscope –** Both **telescopes** and **microscopes** are optical instruments that use lenses (or mirrors) to magnify objects. While a **telescope** helps us observe **distant celestial bodies** , a **microscope** allows us to study **tiny, close objects** invisible to the naked eye. This article explains their **principle, structure, magnifying power** , and differences in a clear and student-friendly way. ## **Introduction to Optical Instruments** Optical instruments are devices that process light to form clear and magnified images of objects. They use **lenses** , **mirrors** , or both to manipulate light rays. The two most important magnifying instruments are: * **Telescope:** For viewing faraway objects (like stars and planets). * **Microscope:** For viewing minute objects (like cells and bacteria). Despite having different purposes, both work on the **principle of refraction of light** through lenses. ## **Part A: Telescope** ## **What Is a Telescope?** A **telescope** is an optical instrument used to observe **distant objects** by collecting and magnifying light. It provides **angular magnification** , making faraway celestial or terrestrial objects appear closer and clearer. **Basic Components:** **Objective lens:** A large convex lens with a long focal length that collects light from distant objects and forms a real image. **Eyepiece lens:** A smaller convex lens with a short focal length that magnifies the image formed by the objective. ## **Working Principle of Telescope** The telescope works on the **refraction of light** and **angular magnification**. * Light from a distant object enters through the **objective lens** , forming a **real, inverted image** at its focal plane. * The **eyepiece lens** acts like a magnifier to enlarge this image for the observer’s eye. * The final image appears **magnified, inverted** , and formed at infinity for comfortable viewing. ## **Magnifying Power of a Telescope** The **magnifying power (m)** of a telescope is defined as: m=βα=f0fe​​ where, * β = angle subtended by the image at the eye * α = angle subtended by the object at the naked eye * f0 = focal length of the objective lens * fe​ = focal length of the eyepiece lens **Example:** If f0=100 cm and fe=1 cm, then m=100/1=100. This means the telescope magnifies 100 times. **Length of Telescope Tube:** L=f0+fe​ ## **Types of Telescopes** ### **A. Refracting Telescope** * Uses two **convex lenses** (objective and eyepiece). * Objective has a large focal length; eyepiece has a small focal length. * The image formed is **real, inverted, and magnified**. * Used for both **terrestrial and astronomical observations**. ### **B. Reflecting Telescope** * Uses a **concave mirror** instead of a lens as the objective. * Avoids chromatic aberration (color distortion). * Provides clearer, sharper images. * Commonly used in **modern astronomy**. ## **Key Features of an Astronomical Telescope** **1. Light-Gathering Power:** Determines how much light the telescope can collect. Larger objectives capture more light, making faint stars visible. **2. Resolving Power:** The ability to distinguish between two closely spaced objects. A larger **diameter of the objective lens** increases resolution. **3. Example:** The largest lens objective telescope is at **Yerkes Observatory (Wisconsin, USA)** , with a diameter of **40 inches (~1.02 m)**. **4. Limitation:** * Large lenses are heavy and hard to support. * Expensive to make without distortions. * Hence, most modern telescopes use **mirrors** instead of lenses. ## **Terrestrial vs Astronomical Telescopes** **Feature**| **Terrestrial Telescope**| **Astronomical Telescope** ---|---|--- **Purpose**| Used to view distant objects on Earth| Used to view celestial objects **Image Formed**| Erect image| Inverted image **Lenses Used**| Has additional inverting lens| No extra lens used **Example**| Spyglass, binoculars| Hubble Space Telescope ## **Part B: Microscope** ## **What Is a Microscope?** A **microscope** is an optical instrument used to view **small, close objects** that cannot be seen clearly with the naked eye. It magnifies the fine details of objects such as microorganisms, cells, and crystals. **Main Parts:** * **Objective lens:** Near the object; forms a real, inverted, magnified image. * **Eyepiece lens:** Magnifies the image produced by the objective to form a final virtual, enlarged image. ## **Working Principle of Microscope** The **microscope** works on the **principle of refraction of light through convex lenses**. * The **objective lens** first creates a **real, inverted, magnified image** of the object. * The **eyepiece lens** then acts like a magnifier to produce a **final enlarged and virtual image**. The combination of both lenses provides **high total magnification**. ## **Magnification in a Microscope** For a **compound microscope** , magnifying power is the **product** of magnifications of both lenses: M=Mobjective×Meyepiece​ Since the objective forms a magnified real image and the eyepiece enlarges it again, overall magnification is very high. **In general:** M∝1f0×fe​ Smaller the focal lengths, greater the magnification. **Practical Note:** In real microscopes, both lenses have **small focal lengths** (less than 1 cm) to achieve large magnification. ## **Types of Microscopes** ### **A. Simple Microscope (Magnifying Glass)** * Consists of a **single convex lens**. * Used for magnifications less than 9×. * Produces **virtual, erect, and enlarged** images. * Example: Reading lenses, jeweller’s lenses. ### **B. Compound Microscope** * Uses **two convex lenses** (objective and eyepiece). * Objective has very short focal length. * Produces **enlarged, inverted, and virtual** images. * Used in laboratories for biological and material study. ## **Ray Diagram for a Compound Microscope** 1. Object placed slightly beyond the **focal point of the objective lens**. 2. Objective forms a **real, inverted, magnified image**. 3. This image acts as an **object for the eyepiece lens**. 4. Eyepiece forms a **virtual, enlarged image** seen by the eye. Hence, the microscope provides **very high magnification and fine detail**. ## **Convex and Concave Lenses** ### **Convex Lens (Converging Lens):** * Converges light rays inward to a focus. * Used in microscopes and telescopes. * Produces **real and inverted** images (in most cases). ### **Concave Lens (Diverging Lens):** * Diverges light rays outward. * Produces **virtual and erect** images. * Used in spectacles and optical corrections. ## **Differences Between Telescope and Microscope** **Feature**| **Telescope**| **Microscope** ---|---|--- **Purpose**| Viewing distant objects| Viewing very small nearby objects **Distance of Object**| Infinite or very far| Very close **Lens Type**| Objective with long focal length| Objective with short focal length **Magnification**| Moderate| Very high **Image Formed**| Inverted and real| Enlarged, inverted, and virtual **Used In**| Astronomy, navigation| Biology, materials science ## **Applications** ### **Telescopes:** * Used in **astronomy** to observe planets, stars, and galaxies. * In **navigation and defense** for distant viewing. * In **satellite communication** and **space research** (e.g., Hubble Space Telescope). ### **Microscopes:** * Used in **medical and biological studies** to observe cells, bacteria, and tissues. * In **forensic science** for trace analysis. * In **material research** for studying crystal structures. ## **Summary** **Instrument**| **Type of Lens Used**| **Purpose**| **Nature of Image**| **Magnification Principle** ---|---|---|---|--- **Telescope**| Convex (or mirror)| View distant objects| Real, inverted| m=f0/fe​ **Microscope**| Two convex lenses| View small close objects| Virtual, inverted| M=Mo×Me ## **FAQ** **Q1. What is the difference between refracting and reflecting telescopes?** A refracting telescope uses lenses, while a reflecting telescope uses mirrors to collect and focus light. **Q2. What is the principle of a microscope?** It works on refraction of light through convex lenses to form magnified virtual images. **Q3. Why is the image in a telescope inverted?** Because the objective lens forms a real image that gets inverted when magnified by the eyepiece. **Q4. What determines the magnifying power of a microscope?** The focal lengths of the objective and eyepiece lenses — shorter focal lengths provide higher magnification. **Q5. Why do astronomers prefer reflecting telescopes?** Mirrors eliminate chromatic aberration, provide clearer images, and are easier to build in large sizes.

How Telescope and Microscope work, their lens systems, magnifying power formulas, and real-life applications in astronomy and biology.