While looking at an image formed by a convex lens (one half of the lens is covered with a black paper), which one of the following will happen to the image?

1. Introduction to Spherical Lenses (basic)

Welcome to your first step in mastering Geometrical Optics. To understand how we see the world through spectacles, telescopes, or even our own eyes, we must first understand the Spherical Lens. Unlike a mirror that reflects light, a lens is a piece of transparent material (like glass or plastic) bound by two surfaces, where at least one surface is spherical. This structure allows light to pass through and bend, a process known as refraction. Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.150

Lenses are categorized based on their shape and how they manipulate light. The two primary types you need to know are Convex and Concave lenses. A convex lens is often called a converging lens because it brings parallel rays of light together at a single point, whereas a concave lens is a diverging lens because it spreads light rays apart. Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.163

Feature	Convex Lens	Concave Lens
Physical Shape	Thicker in the middle, thinner at the edges. Bulges outward.	Thinner in the middle, thicker at the edges. Curved inward.
Effect on Light	Converges (collects) light rays.	Diverges (spreads) light rays.
Common Use	Magnifying glasses, correcting hypermetropia.	Peepholes in doors, correcting myopia.

A fundamental principle that often surprises students is how an image is formed. We often think of light passing through the center of a lens, but in reality, every single point on a lens contributes to the formation of the image. If you were to cover the bottom half of a convex lens with black paper, you might expect only half the object to be visible. However, the lens will still produce a complete image of the object. This is because light rays from every part of the object reach the uncovered top half and converge to form the full picture. The only difference is that the image will be dimmer (less intense) because only half the amount of light is being used to create it.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.150, 157; Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.163

2. Refraction and the Lens Formula (intermediate)

Refraction is fundamentally the change in direction of a light ray as it passes from one transparent medium to another, caused by a change in the speed of light. This phenomenon is governed by Snell’s Law, which states that the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant for a given pair of media. This constant is the Refractive Index Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148. For example, light travels slower in glass (refractive index ~1.50) than in air (~1.0003), causing it to bend toward the normal when entering glass Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.149.

To calculate where an image will form, we use the Lens Formula: 1/v – 1/u = 1/f. Here, u represents the distance of the object from the optical center, v is the distance of the image, and f is the focal length of the lens Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.155. It is crucial to follow the Cartesian sign convention—typically, the object distance (u) is taken as negative because the object is placed to the left of the lens. The ability of a lens to converge or diverge light rays is expressed as its Power (P), calculated as the reciprocal of the focal length in meters (P = 1/f). The SI unit for power is the Dioptre (D); a convex lens has a positive power, while a concave lens has a negative power Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.158.

A common misconception is that blocking a portion of a lens will block a corresponding portion of the image. In reality, every single point on an object emits light rays that strike the entire surface of the lens. Each part of the lens is capable of forming a complete image of the entire object. Therefore, if you cover the lower half of a lens with opaque paper, the rays passing through the top half still converge to form a complete image. The only change is that since only half the light rays are reaching the screen, the image will be significantly dimmer (lower intensity) Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.159.

Sources: Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148; Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.149; Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.155; Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.158; Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.159

3. Spherical Mirrors and Reflection (basic)

Welcome! Today we explore the world of spherical mirrors. Unlike flat plane mirrors, spherical mirrors have reflecting surfaces that are part of a hollow sphere. Depending on which side is polished, we classify them into two main types: concave and convex. You can easily distinguish them by looking at their side profiles: a concave mirror curves inwards like a cave, while a convex mirror bulges outwards Science Class VIII, Light: Mirrors and Lenses, p.155.

The magic of these mirrors lies in how they manipulate light. A concave mirror is often called a converging mirror because it bends light rays inward to a point. It is quite versatile—if you place an object very close to it, you get a large, upright (erect) image (think of a shaving mirror). However, as you move the object further away, the image flips upside down (becomes inverted) and changes size Science Class VIII, Light: Mirrors and Lenses, p.156. In contrast, a convex mirror is a diverging mirror. It always produces an image that is upright and smaller (diminished) than the object, which is why they are perfect for rear-view mirrors in cars—they allow you to see a much wider area behind you.

Feature	Concave Mirror	Convex Mirror
Shape	Reflecting surface curved inwards.	Reflecting surface curved outwards.
Nature of Image	Can be real or virtual; enlarged or diminished.	Always virtual, erect, and diminished.
Common Use	Torches, dentist mirrors, solar furnaces.	Rear-view mirrors in vehicles.

To calculate exactly where an image will form, we use the Mirror Formula. This mathematical relationship connects the focal length (f), the distance of the object from the mirror (u), and the distance of the image from the mirror (v). The formula is expressed as: 1/f = 1/v + 1/u Science Class X, Light – Reflection and Refraction, p.143. When using this formula, we follow the New Cartesian Sign Convention, where distances measured in the direction of incident light are positive, and those against it are negative.

Sources: Science Class VIII, Light: Mirrors and Lenses, p.155; Science Class VIII, Light: Mirrors and Lenses, p.156; Science Class X, Light – Reflection and Refraction, p.143

4. The Human Eye and Vision Defects (intermediate)

The human eye is a biological masterpiece that functions much like a high-end camera. It uses a flexible, crystalline lens to focus light onto a light-sensitive screen known as the retina Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.170. Unlike the glass lenses in your spectacles, the eye lens is a fibrous, jelly-like structure whose curvature can be modified by the ciliary muscles. This unique ability to adjust the focal length is called the Power of Accommodation.

When you gaze at a distant mountain, your ciliary muscles are relaxed, making the lens thin and increasing its focal length. Conversely, when you read a book held at the least distance of distinct vision (about 25 cm for a healthy adult), the ciliary muscles contract, making the lens thicker and decreasing its focal length to ensure the image falls precisely on the retina Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.162.

Vision defects occur when the eye cannot properly converge light onto the retina. The two most common refractive errors are summarized below:

Feature	Myopia (Near-sightedness)	Hypermetropia (Far-sightedness)
Symptom	Can see near objects, but distant objects are blurry.	Can see distant objects, but near objects are blurry.
Image Focus	Forms in front of the retina.	Forms behind the retina.
Cause	Excessive curvature of lens or elongated eyeball.	Focal length too long or eyeball too small.
Correction	Concave lens (Diverging).	Convex lens (Converging).

Another common condition is Presbyopia, which usually occurs with aging. As we grow older, the ciliary muscles weaken and the eye lens loses its flexibility. This leads to a diminished power of accommodation, making it difficult to see nearby objects clearly without corrective lenses Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.163.

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.170

5. Optical Instruments: Microscopes and Telescopes (exam-level)

When we move beyond a single lens to complex optical instruments like microscopes and telescopes, we are essentially looking at "lens systems." Instead of relying on one piece of glass, these instruments use a combination of lenses in contact to improve image quality and magnification. As noted in Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.158, the total power (P) of such a system is the simple algebraic sum of the individual powers (P = P₁ + P₂ + ...). This additive property allows engineers to design systems that minimize optical defects, such as blurring or color fringing, which are common in single-lens setups.

To understand how these instruments work, we must grasp a fundamental principle of image formation: every single point on an object emits an infinite number of light rays that strike every available part of the lens surface. While we often draw only two specific rays in diagrams to locate an image — such as a ray parallel to the principal axis or one passing through the optical center Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.153 — it is vital to remember that the entire lens surface is busy gathering light from the entire object.

This leads us to a fascinating conceptual scenario often tested in exams: What happens if you cover half of a lens with black paper? You might intuitively think that half the image would disappear. However, because every part of the lens receives light from every part of the object, the remaining uncovered half still has enough "information" to converge rays and form a complete image. The geometry of the image (its size, position, and orientation) remains exactly the same. The only change is intensity. Since the total number of light rays contributing to the image is reduced by half, the resulting image will appear significantly dimmer or fainter.

Feature	Full Lens	Half-Covered Lens
Image Completeness	Full image formed	Full image formed
Brightness (Intensity)	High/Normal	Lower (Dimmer)
Image Position/Size	Based on Focal Length	Unchanged

In high-powered laboratory microscopes, these principles are used to ensure maximum light gathering and clarity, whereas low-cost alternatives like the foldscope provide accessibility by using simpler optical arrangements Science, Class VIII, NCERT (Revised ed 2025), The Invisible Living World, p.15. Whether in a telescope peering at stars or a microscope viewing microbes, the core physics remains: the lens area determines brightness, while the lens curvature (focal length) determines the image's geometry.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.152, 153, 158; Science, Class VIII, NCERT (Revised ed 2025), The Invisible Living World: Beyond Our Naked Eye, p.15

6. Image Formation by Convex Lenses (intermediate)

A convex lens, often called a converging lens, works by bending light rays inward toward a common point. To understand how it forms an image, we use ray diagrams, which typically track at least two specific rays: one that travels parallel to the principal axis (passing through the focus after refraction) and one that passes directly through the optical center without any deviation Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.153. The nature of the resulting image—whether it is real or virtual, inverted or erect—depends entirely on the distance of the object from the lens.

As an object moves closer to the lens, the image generally moves further away and grows in size. For instance, when an object is placed at 2F₁ (twice the focal length), the image is formed at 2F₂ on the opposite side, maintaining the same size as the object Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.152. However, if the object is placed very close—specifically between the focus (F₁) and the optical center (O)—the lens can no longer converge the rays on the other side. Instead, the rays appear to diverge from a point behind the object, creating a virtual, erect, and magnified image, which is the principle behind a simple magnifying glass.

Object Position	Image Position	Relative Size	Nature
Beyond 2F₁	Between F₂ and 2F₂	Diminished	Real & Inverted
At 2F₁	At 2F₂	Same Size	Real & Inverted
Between F₁ and 2F₁	Beyond 2F₂	Enlarged	Real & Inverted
Between F₁ and O	Same side as object	Enlarged	Virtual & Erect

A fascinating conceptual nuance occurs when we partially obstruct the lens. A common misconception is that covering half of a lens with black paper will result in "half an image." In reality, every single point on the object sends light rays to every part of the lens surface. Therefore, even if half the lens is blocked, the remaining half still receives rays from the entire object and converges them to form a complete image. The only difference is that since fewer light rays are participating in the formation, the image will appear dimmer (reduced intensity) Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.160.

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

7. Aperture and Intensity of Light (exam-level)

To understand how light behaves in optical systems, we must first define the aperture. In simple terms, the aperture is the effective diameter of the circular outline of a spherical lens or mirror Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.151. Think of it as the 'opening' or the 'window' through which light enters the system. While the focal length determines where an image is formed, the aperture determines how much light is collected. In most standard physics problems, we deal with thin lenses with small apertures, meaning the diameter is much smaller than the lens's radius of curvature Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.137.

The intensity of light in the resulting image is directly proportional to the amount of light energy that passes through this aperture. Specifically, intensity is proportional to the area of the aperture (which depends on the square of the diameter). A larger aperture allows more light rays to converge at the image point, resulting in a brighter image. Conversely, if you restrict the aperture, you reduce the 'photon count' reaching the screen, making the image dimmer.

A common conceptual challenge in competitive exams is the 'blocked lens' scenario: What happens if you cover the bottom half of a convex lens with black paper? Many students mistakenly believe only half the image will be visible. However, since every point on an object emits light rays that hit every part of the lens surface, the rays passing through the remaining top half are still sufficient to form a complete image of the entire object. The only change is that because fewer total rays reach the destination, the image will have significantly lower intensity (it will appear fainter or less bright) Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.152.

Feature	Effect of Large Aperture	Effect of Small/Blocked Aperture
Image Completeness	Full image formed	Full image formed (regardless of blockage)
Image Brightness	High Intensity (Bright)	Low Intensity (Dim)
Light Gathering Power	High	Low

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.151; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.137; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.152

8. Solving the Original PYQ (exam-level)

This question perfectly tests your understanding of the principle of light propagation and image formation. Having just mastered the building blocks of how light rays converge, you must remember that every single point on an object radiates light rays in infinite directions. When these rays strike a convex lens, every available part of the lens surface participates in refracting those rays to form the entire image. Even if you block half the lens, the remaining uncovered portion still receives light from every point of the object and refracts it to the same focal point, as explained in NCERT Class 10 Science.

To arrive at the correct reasoning, consider the lens as a gateway for energy. By covering half of it with black paper, you have not changed the focal length or the object distance, which are the variables that determine the size and orientation of an image. Instead, you have simply reduced the aperture area—the total surface through which light can pass. Because fewer rays are now reaching the screen to form the image, the Intensity of the image will be diminished. The image remains complete and upright/inverted as before, but it will appear significantly fainter because the total "light budget" has been cut in half.

UPSC often uses intuitive traps like Option (A) to see if you can distinguish between the physical area of the lens and the geometry of the image. It is a common misconception that half a lens produces half an image; however, optics proves that area only affects brightness. Similarly, Options (C) and (D) are incorrect because the magnification and nature of the image are properties of the lens's curvature and position, not how much of its surface is exposed. Always remember: blocking the lens affects the quality (brightness) of the image, not its topology (shape and size).