An object is kept 5 cm in front of a concave mirror of focal length 15 cm. What will be the nature of the image?

1. Light: Fundamentals and Laws of Reflection (basic)

At its most fundamental level, light is an electromagnetic wave that allows us to see the world. One of its most predictable behaviors is that it tends to travel in straight lines, a property known as rectilinear propagation Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p. 158. When light hits a highly polished surface like a mirror, it doesn't just pass through; it bounces back. This phenomenon is called reflection. Whether the surface is as flat as a bathroom mirror or as curved as a stainless steel spoon, the way light bounces is governed by two universal rules known as the Laws of Reflection.

These laws state that:

• Law 1: The angle of incidence (the angle at which the light hits the surface) is always equal to the angle of reflection (the angle at which it bounces off). Both angles are measured from an imaginary line called the 'normal,' which is perpendicular to the surface at the point of impact.
• Law 2: The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p. 135.

The beauty of these laws is their universality—they apply to all types of reflecting surfaces, including the spherical mirrors we will study in later hops.

When light reflects, it forms an image. In a standard plane mirror, the image has very specific characteristics: it is virtual (it appears to be behind the mirror where light doesn't actually go), erect (upright), and exactly the same size as the object Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p. 135. You will also notice lateral inversion, where your right side appears as the left side of the image Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p. 156.

Feature	Plane Mirror Image	Spherical Mirror Image
Size	Always same as object	Can be magnified, diminished, or same
Nature	Always virtual and erect	Can be real/inverted or virtual/erect
Laws of Reflection	Applicable	Applicable

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.134, 135, 158; Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.156

2. Spherical Mirrors: Basic Terminology (basic)

To understand how light behaves when it hits a curved surface, we must first master the geography of a spherical mirror. Imagine a hollow glass sphere. If you cut out a piece and coat one side with silver, you create a spherical mirror. The geometric center of this mirror's reflecting surface is called the Pole (P). Think of the pole as the 'origin' or the starting point for all our measurements Science, Light – Reflection and Refraction, p.136.

Since the mirror is a slice of a sphere, that sphere has a center, known as the Center of Curvature (C). The distance from the center to the pole is the Radius of Curvature (R). An imaginary straight line passing through both P and C is the Principal Axis. A critical rule to remember is that the principal axis is always normal (perpendicular) to the mirror at its pole. The effective diameter of the reflecting surface—essentially the 'mouth' of the mirror—is called its Aperture Science, Light – Reflection and Refraction, p.137.

When parallel rays of light strike a mirror, they reflect and either converge at or appear to diverge from a specific point on the principal axis called the Principal Focus (F). For mirrors with a small aperture, this focus lies exactly halfway between the pole and the center of curvature. This gives us the fundamental mathematical relationship: R = 2f, where f is the focal length Science, Light – Reflection and Refraction, p.137. We use a standard Cartesian Sign Convention to keep our calculations consistent:

• The Pole (P) is treated as the origin.
• Distances measured in the direction of incident light (to the right) are positive.
• Distances measured against the direction of incident light (to the left) are negative.
• Heights above the principal axis are positive; heights below are negative Science, Light – Reflection and Refraction, p.142.

Term	Symbol	Definition
Pole	P	The geometric center of the mirror surface.
Principal Focus	F	The point where parallel rays meet or seem to come from.
Focal Length	f	The distance between the Pole and the Principal Focus.

Sources: Science, Light – Reflection and Refraction, p.136; Science, Light – Reflection and Refraction, p.137; Science, Light – Reflection and Refraction, p.142

3. Refraction and Snell's Law (intermediate)

While reflection involves light bouncing off a surface, refraction describes how light behaves when it passes from one transparent medium into another. The fundamental reason light bends during this transition is a change in its speed. Light travels fastest in a vacuum (approximately 3 × 10⁸ m/s), and while its speed in air is only marginally less, it slows down significantly when entering denser materials like water or glass Science, Class X (NCERT 2025 ed.), Chapter 9, p.148. This change in speed causes the light ray to change direction at the interface of the two media.

Refraction follows two specific laws that allow us to predict exactly how a ray will behave:

• The First Law: The incident ray, the refracted ray, and the "normal" (an imaginary line perpendicular to the surface) at the point of incidence all lie in the same plane Science, Class X (NCERT 2025 ed.), Chapter 9, p.148.
• The Second Law (Snell’s Law): For a given pair of media and a specific color of light, the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant. Mathematically, this is expressed as: sin i / sin r = constant.

This constant is known as the refractive index of the second medium with respect to the first. The refractive index (n) is not just an arbitrary number; it represents the ratio of the speed of light in the two media. For example, the refractive index of medium 2 with respect to medium 1 (n₂₁) is calculated as the speed of light in medium 1 (v₁) divided by the speed of light in medium 2 (v₂) Science, Class X (NCERT 2025 ed.), Chapter 9, p.148.

Scenario	Change in Speed	Direction of Bending
Rarer to Denser (e.g., Air to Glass)	Speed Decreases	Bends towards the normal
Denser to Rarer (e.g., Glass to Air)	Speed Increases	Bends away from the normal

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.148; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.159

4. Total Internal Reflection (TIR) and Applications (intermediate)

Imagine light trying to escape from a swimming pool into the air. Usually, it refracts and bends away from the normal because it is moving from an optically denser medium (water) to an optically rarer medium (air) Science, Light – Reflection and Refraction, p.149. However, if the light hits the surface at a very shallow angle, it doesn't escape at all; instead, it reflects back into the water like it hit a mirror. This is Total Internal Reflection (TIR). Unlike ordinary reflection from a mirror, where some light is always absorbed, TIR is "total" because nearly 100% of the light energy is retained, making it incredibly efficient for technology.

For TIR to happen, two strict conditions must be met. First, the light must be traveling from a denser medium to a rarer medium. Second, the angle of incidence must be greater than a specific threshold called the Critical Angle (θc). As the angle of incidence increases, the refracted ray bends further away from the normal until it eventually grazes the boundary surface (angle of refraction = 90°). This specific incident angle is the Critical Angle. If you increase the angle even slightly more, Snell's Law Science, Light – Reflection and Refraction, p.148 can no longer be satisfied by refraction, and the light is forced to reflect internally.

Scenario	Angle of Incidence (i)	Result
Refraction	i < Critical Angle	Light bends away from the normal into the rarer medium.
Critical Stage	i = Critical Angle	Light grazes the interface (refraction angle is 90°).
TIR	i > Critical Angle	Light is 100% reflected back into the denser medium.

In the modern world, TIR is the backbone of global communication. Optical fiber cables use TIR to transmit vast amounts of data over thousands of kilometers FUNDAMENTALS OF HUMAN GEOGRAPHY, Transport and Communication, p.68. Because the light reflects off the inner walls of the fiber with almost zero loss, we can send high-speed internet signals across oceans. Other common examples include the brilliance of diamonds (where light is trapped inside by multiple TIRs) and mirages seen on hot roads, caused by light bending through layers of air with different optical densities.

Sources: Science, Light – Reflection and Refraction, p.148; Science, Light – Reflection and Refraction, p.149; FUNDAMENTALS OF HUMAN GEOGRAPHY, Transport and Communication, p.68

5. Spherical Lenses and Power (intermediate)

Welcome! Now that we’ve explored how light reflects off mirrors, we move to Refraction through Spherical Lenses. While mirrors reflect light, lenses are transparent materials (usually glass) that bend light as it passes through them. A lens is formed by binding two transparent surfaces, where at least one surface is spherical Science, Light – Reflection and Refraction, p.152.

Lenses come in two primary flavors based on how they treat light rays. A Convex Lens is thicker at the middle than at the edges; it converges parallel rays to a point, which is why we call it a converging lens. Conversely, a Concave Lens is thinner at the middle and thicker at the edges; it spreads light rays apart, earning it the name diverging lens. Just like mirrors, lenses have a Principal Focus (F) and a Focal Length (f), but because light can pass through a lens from either side, every lens has two focal points.

Feature	Convex Lens	Concave Lens
Action on Light	Converging	Diverging
Focal Length (f)	Positive (+)	Negative (–)
Nature of Image	Real & Inverted (mostly); Virtual & Erect (when object is very close)	Always Virtual, Erect, and Diminished

To solve numerical problems, we use the Lens Formula, which relates the object distance (u), image distance (v), and focal length (f): 1/v – 1/u = 1/f Science, Light – Reflection and Refraction, p.155. Notice the minus sign! This is the primary mathematical difference from the mirror formula. Additionally, we talk about the Power of a Lens (P), which describes its ability to converge or diverge light. Power is simply the reciprocal of the focal length in meters (P = 1/f). Its SI unit is the Dioptre (D) Science, Light – Reflection and Refraction, p.159.

Sources: Science, Light – Reflection and Refraction, p.152; Science, Light – Reflection and Refraction, p.153; Science, Light – Reflection and Refraction, p.155; Science, Light – Reflection and Refraction, p.159

6. Concave Mirror: Case-wise Image Formation (intermediate)

A concave mirror, often called a converging mirror, is unique because the nature of the image it forms changes dramatically based on where the object is placed relative to the mirror's Principal Focus (F) and Center of Curvature (C). Unlike convex mirrors, which always produce small, virtual images, a concave mirror can create images that are real or virtual, magnified or diminished, and erect or inverted. To understand this, we typically use ray diagrams, selecting two specific rays (like one parallel to the principal axis and one passing through the center of curvature) to see where they intersect after reflection Science, Class X (NCERT 2025 ed.), Chapter 9, p.138.

For most positions—when the object is at infinity, beyond C, at C, or between C and F—the reflected rays actually meet in front of the mirror, forming a real and inverted image. As the object moves closer to the mirror, the image generally moves further away and grows in size. For instance, when the object is placed exactly at C, the image is also at C and is exactly the same size as the object. However, the most critical transition occurs when the object crosses the Principal Focus (F) and moves very close to the mirror Science, Class VIII (NCERT 2025 ed.), Chapter 13, p.156.

When an object is placed between the Pole (P) and the Focus (F)—meaning the object distance (u) is less than the focal length (f)—the reflected rays diverge and never meet in front of the mirror. Instead, they appear to meet behind the mirror when traced backward. This results in a virtual, erect, and magnified image. This specific property is why concave mirrors are used as shaving mirrors or dentist mirrors; they provide an enlarged view of the object when held close. Mathematically, using the mirror formula 1/f = 1/v + 1/u, when u < f, the image distance (v) becomes positive, confirming the image is behind the mirror Science, Class X (NCERT 2025 ed.), Chapter 9, p.143.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.138, 139, 143; Science, Class VIII (NCERT 2025 ed.), Chapter 13: Light, p.156

7. Mirror Formula and Sign Convention (exam-level)

In geometrical optics, we move beyond drawing ray diagrams to using mathematical precision. To calculate exactly where an image will form and how large it will be, we use the Mirror Formula. However, math requires a consistent coordinate system, which we call the New Cartesian Sign Convention. In this system, the Pole (P) of the mirror is treated as the origin (0,0), and the principal axis is the x-axis Science, Light – Reflection and Refraction, p.142.

Under this convention, the object is always placed to the left of the mirror, meaning the object distance (u) is always taken as negative. Distances measured in the direction of the incident light (to the right of the pole) are positive, while those measured against it (to the left) are negative. Heights above the principal axis are positive, and those below are negative. This leads to a crucial rule: the focal length (f) of a concave mirror is always negative, while that of a convex mirror is always positive Science, Light – Reflection and Refraction, p.143.

The Mirror Formula provides the quantitative link between the object distance (u), image distance (v), and focal length (f):

1/v + 1/u = 1/f

When you solve for v, its sign tells you the nature of the image. A negative v means the image is formed in front of the mirror (real), while a positive v means it is formed behind the mirror (virtual). To determine the size, we use Magnification (m), defined as the ratio of image height (h′) to object height (h), which also equals -v/u Science, Light – Reflection and Refraction, p.159.

Quantity	Concave Mirror	Convex Mirror
Focal Length (f)	Always Negative (–)	Always Positive (+)
Object Distance (u)	Always Negative (–)	Always Negative (–)
Image Distance (v)	Negative (Real) or Positive (Virtual)	Always Positive (Virtual)

Sources: Science, Light – Reflection and Refraction, p.142; Science, Light – Reflection and Refraction, p.143; Science, Light – Reflection and Refraction, p.159

8. Solving the Original PYQ (exam-level)

This question perfectly tests your mastery of sign conventions and the specific ray diagram properties of a concave mirror. Having just completed the building blocks of optics, you can identify that the object distance (u = 5 cm) is less than the focal length (f = 15 cm). This puts the object in the unique "Case 6" position: between the Pole (P) and the Principal Focus (F). While concave mirrors typically converge light to form real images, this specific placement causes the reflected rays to diverge, meaning they never meet in front of the mirror but appear to intersect behind it.

To arrive at the answer systematically, think about the Mirror Formula and the resulting magnification. When the object is within the focal length, the image distance (v) calculated will be positive, indicating the image is formed behind the mirror—the very definition of a virtual image. Because the reflected rays spread outwards, the image formed behind the mirror is logically larger than the object itself. Therefore, the nature of the image is Virtual, magnified, making (B) the correct answer. This is the same principle used in shaving mirrors or dental mirrors to see a larger, upright view of a small area, as explained in Science, class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction.

UPSC often includes options like (C) and (D) to trip up students who jump to the conclusion that a concave mirror always produces a real image; remember, real images only form when the object is at or beyond the focal point (u ≥ f). Option (A) is another classic trap—a virtual but diminished image is a defining characteristic of convex mirrors, not concave ones. Distinguishing between these specific boundary conditions is the key to avoiding marks lost to common conceptual overlaps.