Which of the following statements about optical microscope is/are correct? 1. Both the eyepiece and objective of a microscope are convex lenses. 2. The magnification of a microscope increases with increase in focal length of the objective. 3. The magnification of a microscope depends upon the length of the microscope tube, 4. The eyepiece of a microscope is a concave lens. Select the correct answer using the code given below.

1. Basics of Spherical Lenses: Convex vs. Concave (basic)

Welcome to the first step in our journey through Geometrical Optics. To understand complex instruments like telescopes or microscopes, we must first master the basic building block: the spherical lens. A lens is a piece of transparent material (like glass) bound by two surfaces, where at least one surface is spherical. Unlike mirrors which reflect light, lenses work through refraction—the bending of light as it passes from one medium to another.

There are two primary types of spherical lenses you need to recognize instantly: Convex and Concave. A Convex lens (also called a double convex lens) bulges outwards and is physically thicker at the middle than at the edges. Its superpower is convergence: when parallel rays of light pass through it, they are bent inward to meet at a single point called the focus Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.150. Conversely, a Concave lens is curved inwards, making it thicker at the edges than in the middle. It acts as a diverging lens, spreading light rays apart as if they were coming from a point behind the lens.

Feature	Convex Lens	Concave Lens
Physical Shape	Thicker in the center; bulges out.	Thinner in the center; curves in.
Effect on Light	Converging (bends rays together).	Diverging (spreads rays apart).
Common Alias	Converging Lens	Diverging Lens

The degree to which a lens can bend light is determined by its focal length. A lens with a short focal length is more powerful because it bends light rays at sharper angles, focusing them much closer to the center of the lens Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.157. This relationship is captured by the concept of Power (P), which is simply the reciprocal of the focal length (P = 1/f). When you are reading small print in a dictionary, you prefer a convex lens with a short focal length because it provides higher magnification and stronger light-bending capability Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.160.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.150; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.157; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.160

2. Image Formation by Convex Lenses (basic)

A convex lens, often called a converging lens, is thicker at the center than at the edges. When parallel rays of light pass through it, they converge at a single point called the principal focus (F). To understand how images are formed, we rely on ray diagrams, which use specific paths of light to predict where an image will appear. According to standard optical principles, three primary rays are used: (1) a ray parallel to the principal axis passes through the focus on the other side; (2) a ray passing through the optical center (O) goes straight without deviation; and (3) a ray passing through the focus emerges parallel to the principal axis Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.153.

The nature and size of the image produced by a convex lens are not fixed; they change dynamically based on the object's distance from the lens. As you move an object closer to the lens from infinity, the image moves further away from the lens and grows in size. This behavior is summarized in the table below:

Object Position	Image Position	Size of Image	Nature of Image
At infinity	At focus F₂	Highly diminished (point)	Real and Inverted
Beyond 2F₁	Between F₂ and 2F₂	Diminished	Real and Inverted
At 2F₁	At 2F₂	Same size	Real and Inverted
Between F₁ and 2F₁	Beyond 2F₂	Enlarged (magnified)	Real and Inverted
Between F₁ and O	Same side as object	Enlarged (magnified)	Virtual and Erect

Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.152. Note the critical transition: for most positions, the image is real and inverted (it can be projected on a screen). However, once the object crosses the focal point (F₁) and moves very close to the lens, the image becomes virtual and erect. This specific setup is what allows a convex lens to act as a simple magnifying glass.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.152; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.153

3. The Simple Microscope and Human Vision (intermediate)

To understand complex optical instruments, we must first master the simplest one: the magnifying glass, technically known as a simple microscope. At its heart, a simple microscope is nothing more than a single convex lens—a transparent material that is thicker at the middle than at the edges Science, Class VIII, Light: Mirrors and Lenses, p.162. Its magic lies in its ability to bend light rays inward, allowing us to see a virtual, upright, and enlarged image of a small object when it is held close to the lens.

However, the performance of any microscope is limited by the biology of the human eye. Our eyes have a natural lens that can change its shape to focus on objects at different distances, a process called accommodation Science, Class X, The Human Eye and the Colourful World, p.170. But there is a limit: if you bring a book too close to your face, the text becomes a blur. This limit is known as the Least Distance of Distinct Vision (or the near point), which is approximately 25 cm for a healthy young adult Science, Class X, The Human Eye and the Colourful World, p.162. A simple microscope works by allowing you to bring an object very close to your eye while creating an image that appears to be at a comfortable distance (like 25 cm) or further, where the eye can focus without strain.

Feature	Normal Vision (Unaided)	Simple Microscope (Aided)
Min. Object Distance	25 cm (Near Point)	Much less than 25 cm
Image Type	Real image on the retina	Magnified Virtual Image
Lens Type	Biological crystalline lens	External Convex lens

When the eye cannot properly focus light onto the retina, we encounter refractive defects. For instance, in myopia (short-sightedness), the image of a distant object forms in front of the retina rather than on it, requiring a concave lens for correction Science, Class X, The Human Eye and the Colourful World, p.170. Understanding how single lenses correct or magnify vision is the essential foundation for our next step: combining lenses to build a compound microscope.

Sources: Science, Class VIII, Light: Mirrors and Lenses, p.162; Science, Class X, The Human Eye and the Colourful World, p.170; Science, Class X, The Human Eye and the Colourful World, p.162

4. Applications: Correcting Vision Defects (intermediate)

In a healthy eye, the crystalline lens adjusts its focal length to focus light exactly onto the retina. However, when the eye loses its power of accommodation or when the eyeball's shape is physically mismatched with the lens's focusing power, vision becomes blurred. These are known as refractive defects Science, Class X, p.162. To correct these, we use corrective lenses that modify the path of incoming light so the final image falls precisely on the retina.

The two most common defects are Myopia and Hypermetropia. In Myopia (near-sightedness), the eye's refractive power is too strong or the eyeball is too long, causing light from distant objects to converge in front of the retina. Conversely, in Hypermetropia (far-sightedness), the focal length is too long or the eyeball is too short, causing the image of nearby objects to form behind the retina Science, Class X, p.163. We use the principles of diverging and converging lenses to shift these focal points back onto the retinal surface.

Feature	Myopia (Near-sightedness)	Hypermetropia (Far-sightedness)
Image formed...	In front of the retina	Behind the retina
Cause	High curvature of lens / Long eyeball	Low curvature (long focal length) / Short eyeball
Correction Lens	Concave (Diverging)	Convex (Converging)
Lens Power	Negative (−)	Positive (+)

As we age, we may also develop Presbyopia. This occurs due to the gradual weakening of the ciliary muscles and the hardening of the eye lens, making it difficult to focus on nearby objects Science, Class X, p.164. Interestingly, some individuals suffer from both defects simultaneously. For them, bi-focal lenses are prescribed: the upper part is a concave lens for distant vision, while the lower part is a convex lens for reading and near vision Science, Class X, p.164.

Sources: Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.162; Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.163; Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.164

5. Optical Instruments: The Refracting Telescope (intermediate)

While a microscope helps us see the very small, the Refracting Telescope is designed to observe objects that are very far away, such as stars and planets. To achieve this, it uses a combination of two convex (converging) lenses: the objective and the eyepiece. As noted in Science, Class VIII NCERT, Light: Mirrors and Lenses, p.165, telescopes are essential tools that utilize lenses to help us see distant things clearly, though we must never use them to look directly at the sun to avoid eye damage.

The lens system works in two distinct stages. The objective lens, which faces the distant object, has a large aperture and a long focal length (fₒ). Its primary job is to collect as much light as possible from the distant source and form a real, inverted image at its focal plane. The eyepiece, which has a shorter focal length (fₑ), then acts as a simple magnifier to enlarge this intermediate image, creating a final virtual image for the observer. The diameter of the lens, known as the aperture, is crucial here; a larger aperture allows the telescope to resolve finer details by capturing more light Science, Class X NCERT, Light – Reflection and Refraction, p.137.

The magnifying power (M) of a refracting telescope in normal adjustment (where the final image is at infinity) is calculated by the ratio of the focal lengths: M = fₒ / fₑ. This relationship tells us something vital: to get a highly magnified view of a planet, we need an objective lens with a very long focal length and an eyepiece with a very short focal length. This is why professional refracting telescopes are often housed in very long tubes! In modern optics, these lenses are often used in combinations to minimize distortions and produce the sharpest possible image Science, Class X NCERT, Light – Reflection and Refraction, p.158.

Feature	Objective Lens	Eyepiece Lens
Focal Length	Long (fₒ)	Short (fₑ)
Aperture Size	Large (to collect light)	Small (relative to objective)
Function	Forms the primary image	Magnifies the primary image

Sources: Science, Class VIII NCERT, Light: Mirrors and Lenses, p.165; Science, Class X NCERT, Light – Reflection and Refraction, p.137; Science, Class X NCERT, Light – Reflection and Refraction, p.158

6. The Compound Microscope: Construction and Physics (exam-level)

When we need to see tiny structures like cells or microorganisms, a simple magnifying glass falls short. This is where the Compound Microscope comes in. Unlike a simple microscope, which uses one lens, the compound microscope uses a system of two converging (convex) lenses to achieve much higher magnification. As we know from lens theory, combining lenses allows us to design systems that minimize defects and multiply power Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.158.

The construction involves two key components:

• Objective Lens: This is the lens closest to the specimen. It has a very short focal length (fₒ) and a small aperture. Its job is to form a real, inverted, and magnified image of the object.
• Eyepiece (Ocular): This is the lens closest to the eye. It has a larger focal length (fₑ) and aperture compared to the objective. It acts as a simple magnifier, taking the image formed by the objective and enlarging it further into a final virtual image.

The physics of the compound microscope relies on a two-stage magnification. The objective lens forms the first image (I₁) just inside the focal point of the eyepiece. Because the object is placed just beyond the focal length of the objective, the resulting image is real and magnified Science, Class VIII, Light: Mirrors and Lenses, p.163. The eyepiece then treats this image as its own object to create the final image (I₂), which is virtual, enlarged, and inverted with respect to the original specimen.

Feature	Objective Lens	Eyepiece Lens
Position	Near the specimen	Near the eye
Focal Length	Very small (fₒ)	Larger (fₑ)
Role	Forms real, magnified image	Forms final virtual image

The Total Magnification (M) is the product of the magnification of the objective (mₒ) and the eyepiece (mₑ). Mathematically, it is approximately given by:

M ≈ (L / fₒ) × (D / fₑ)

Where L is the tube length (distance between the two lenses) and D is the least distance of distinct vision (usually 25 cm). This formula reveals a critical rule for microscopy: to increase magnification, you must decrease the focal length of the objective lens. Since magnification is the ratio of image height to object height (m = h′/h), using lenses with higher power (shorter focal lengths) leads to a much larger final visual Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.156.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.156, 158; Science, Class VIII (NCERT Revised ed 2025), Light: Mirrors and Lenses, p.163

7. Solving the Original PYQ (exam-level)

Review the concepts above and try solving the question.