A person standing 1 m in front of a plane mirror approaches the mirror by 40 cm. The new distance between the person and his image in the plane mirror is

1. Fundamental Laws of Reflection (basic)

Welcome to your first step in mastering Geometrical Optics! To understand how we see ourselves in a mirror or how a telescope works, we must start with the most fundamental behavior of light: Reflection. When light traveling through a medium strikes a highly polished surface—like a silvered mirror—it bounces back into the same medium. This phenomenon follows two strict rules known as the Laws of Reflection.

First, let’s define the Normal. Imagine a line perpendicular (90°) to the reflecting surface at the exact point where the light hits. This imaginary line is our reference point. The first law states that the angle of incidence (∠i) is always equal to the angle of reflection (∠r). This means if a ray of light strikes a mirror at an angle of 30° relative to the normal, it will bounce off at exactly 30° on the other side Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.135. Interestingly, if light hits the mirror directly along the normal (at 0°), it reflects back exactly along the same path Science, Class VIII (NCERT 2025 ed.), Light: Mirrors and Lenses, p.158.

The second law is about geometry: the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane. Think of this like a flat sheet of paper; you cannot have the light hit the mirror and then bounce "up" out of that flat sheet. These laws are universal—they apply to flat plane mirrors and curved spherical mirrors alike Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.135.

In a plane mirror, these laws create a very specific type of image. The image is virtual (it appears behind the mirror where light doesn't actually reach) and erect (upright). A crucial property for your competitive exams is symmetry: the distance of the image from the mirror is always equal to the distance of the object from the mirror. If you stand 2 meters away from a mirror, your image is also 2 meters "inside" the mirror, making the total distance between you and your image 4 meters.

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

2. Characteristics of Images in Plane Mirrors (basic)

Imagine standing in front of your dressing table mirror. The image you see is a result of the laws of reflection being applied to a perfectly flat surface. Unlike curved mirrors that can distort your reflection, a plane mirror produces an image that is a perfect 'geometric twin' in terms of dimensions. As noted in Science, Class X NCERT (2025 ed.), Light – Reflection and Refraction, p.135, this image is always virtual and erect. 'Virtual' means the light rays don't actually converge behind the glass; your brain simply perceives them as coming from a point inside the mirror. Consequently, you cannot project this image onto a screen. One of the most critical properties for competitive exams is the symmetry of distance. The image is formed at the exact same distance behind the mirror as the object is in front of it. If you move, your image moves in tandem to maintain this equality. This leads to a vital calculation rule: the total distance between an object and its image is always double the distance between the object and the mirror. Furthermore, the size of the image is exactly equal to the size of the object (Science, Class VIII NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.156). If you are 5 feet tall, your image is 5 feet tall—no more, no less. Finally, we must consider lateral inversion. While the image is erect (it is not upside down), it is reversed sideways. If you raise your right hand, your image appears to raise its left hand. This unique property is why the word 'AMBULANCE' is painted in reverse on the front of emergency vehicles—so that drivers looking in their plane rearview mirrors can read the word correctly.

Feature	Characteristics in a Plane Mirror
Nature	Virtual and Erect (upright)
Size	Identical to the object (Magnification = 1)
Position	Distance of object from mirror = Distance of image from mirror
Orientation	Laterally inverted (Left becomes Right)

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

3. Spherical Mirrors: Concave and Convex (intermediate)

To understand spherical mirrors, imagine a hollow glass sphere. If you cut a small slice out of this sphere and silver one side, you create a curved reflecting surface. Unlike a plane mirror, which is flat, spherical mirrors have surfaces that are part of a sphere. We classify them into two primary types based on which side is reflecting: Concave (curved inwards, like the cave of a spoon) and Convex (curved outwards, like the back of a spoon). Identifying them is simple: if the reflecting surface faces the center of the sphere it was cut from, it is concave; if it faces away, it is convex Science, Class VIII (NCERT), Light: Mirrors and Lenses, p.155.

The behavior of light changes dramatically between these two. A concave mirror is known as a converging mirror because it reflects parallel rays of light inward toward a single point called the principal focus. This mirror is highly versatile: if you place an object very close to it, you get an enlarged, upright (erect) image—perfect for shaving or makeup mirrors. However, as you move the object further away, the image eventually flips and becomes inverted and smaller Science, Class VIII (NCERT), Light: Mirrors and Lenses, p.156. In contrast, a convex mirror is a diverging mirror. It spreads light rays apart. Its superpower is consistency: no matter how far or close an object is, a convex mirror always produces an image that is erect (upright) and diminished (smaller) Science, Class VIII (NCERT), Light: Mirrors and Lenses, p.165. This is why they are used as rear-view mirrors in vehicles; they allow a much wider field of view.

For more advanced analysis, we use the Mirror Formula to calculate exactly where an image will form. This relationship is expressed as 1/v + 1/u = 1/f, where u is the object distance, v is the image distance, and f is the focal length (the distance from the mirror's pole to its focus) Science, Class X (NCERT), Light – Reflection and Refraction, p.143. Importantly, the laws of reflection (angle of incidence equals angle of reflection) still apply perfectly to every single point on these curved surfaces, just as they do for plane mirrors.

Sources: Science, Class VIII (NCERT), Light: Mirrors and Lenses, p.155; Science, Class VIII (NCERT), Light: Mirrors and Lenses, p.156; Science, Class VIII (NCERT), Light: Mirrors and Lenses, p.165; Science, Class X (NCERT), Light – Reflection and Refraction, p.143

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

To solve problems in optics without confusion, we use a standardized system called the New Cartesian Sign Convention. Think of the mirror's pole (P) as the origin (0,0) on a graph, and the principal axis as the x-axis Science, Light – Reflection and Refraction, p.142. By convention, we always place the object to the left of the mirror. This means light always travels from left to right. Consequently, any distance measured in the direction of the incident light (to the right of the pole) is positive, while distances measured against it (to the left) are negative. Similarly, heights measured upward from the principal axis are positive, and those downward are negative Science, Light – Reflection and Refraction, p.143. Once the signs are clear, we use the Mirror Formula to find the position of an image. This formula defines the mathematical relationship between the object distance (u), the image distance (v), and the focal length (f). It is expressed as:

1/v + 1/u = 1/f

This formula is universal; it works for both concave and convex mirrors, regardless of the object's position Science, Light – Reflection and Refraction, p.143. However, the secret to getting the right answer in UPSC-level physics is consistency—you must plug in the values of u, v, and f with their correct signs according to the convention.

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

Sources: Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.142; Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.143

5. Refraction and Total Internal Reflection (intermediate)

When light travels from one transparent medium into another, it doesn't always continue in a straight line; it usually bends at the boundary. This phenomenon is called refraction. The primary cause of this bending is the change in the speed of light as it moves between materials of different optical densities. For instance, light travels fastest in a vacuum (3 × 10⁸ m/s) and slows down slightly in air, and considerably more in glass or water Science, Class X, p.148. This relationship is quantified by the Refractive Index (n), which is the ratio of the speed of light in a vacuum to its speed in the specific medium (n = c/v) Science, Class X, p.159.

Refraction follows two fundamental laws. First, the incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane. Second, known as Snell’s Law, 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 (sin i / sin r = constant) Science, Class X, p.148. This constant represents the refractive index of the second medium relative to the first. When light moves from an optically rarer medium (like air) to a denser medium (like glass), it bends towards the normal. Conversely, moving from dense to rare, it bends away from the normal.

An extraordinary phenomenon occurs when light attempts to travel from a denser medium to a rarer medium (e.g., from water to air). As the angle of incidence increases, the angle of refraction also increases, bending further away from the normal. Eventually, we reach a specific angle of incidence called the Critical Angle, where the refracted ray grazes the surface (r = 90°). If the angle of incidence is increased beyond this critical angle, the light does not pass into the second medium at all; instead, it is reflected entirely back into the denser medium. This is called Total Internal Reflection (TIR). This principle is what makes diamonds sparkle so brilliantly and allows high-speed data to travel through optical fibers.

Condition	Direction of Bending	Result
Rarer to Denser	Towards the Normal	Light slows down
Denser to Rarer (i < Critical Angle)	Away from the Normal	Standard Refraction
Denser to Rarer (i > Critical Angle)	Reflected Back	Total Internal Reflection

Sources: Science, Class X, Light – Reflection and Refraction, p.148; Science, Class X, Light – Reflection and Refraction, p.159

6. Relative Motion and Distance in Plane Mirrors (exam-level)

To master the physics of mirrors, we must first internalize a fundamental symmetry: in a plane mirror, the object distance (u) is always exactly equal to the image distance (v). As observed in Science-Class VII, Light: Shadows and Reflections, p.161, the image appears to be at the same distance behind the mirror as the object is in front of it. This creates a 'mirror image' of the physical space. Because of this 1:1 ratio, the magnification of a plane mirror is always +1, meaning the image is the same size as the object and upright Science, class X, Light – Reflection and Refraction, p.160.

When we discuss relative motion, this symmetry leads to a 'doubling effect.' If you move closer to a mirror by a distance x, your image also moves closer to the mirror by x. Consequently, the total distance between you and your image decreases by 2x. This is why, if you run toward a mirror at a speed of 5 m/s, your image appears to be rushing toward you at a relative speed of 10 m/s. The mirror acts as a fixed reference point, but the distance between the two 'entities' (object and image) changes twice as fast as the distance between the object and the mirror.

Let’s look at how these distances interact:

Scenario	Object to Mirror (u)	Mirror to Image (v)	Object to Image (u + v)
Initial Position	100 cm	100 cm	200 cm
Move 40 cm closer	60 cm	60 cm	120 cm (1.2 m)

Sources: Science-Class VII, Light: Shadows and Reflections, p.161; Science, class X, Light – Reflection and Refraction, p.160

7. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental laws of reflection, this PYQ tests your ability to apply the principle of symmetry in plane mirrors. The core building block here is the concept that the object distance (u) from the mirror is always equal to the image distance (v) behind the mirror. This question essentially asks you to perform a two-step mental mapping: first, calculate the new position of the person, and second, realize that the total distance between the person and the image is the sum of both the object and image distances (u + v).

Walking through the logic: the person starts at 1 m (100 cm) and moves 40 cm closer, making the new object distance 60 cm. Since the mirror reflects symmetrically, the image is also 60 cm behind the mirror surface. Therefore, the total separation is 60 cm + 60 cm = 120 cm. Converting this back to meters gives 1.2 m. It is worth noting that UPSC often uses dashes in options to represent decimal points (e.g., 1-2 m for 1.2 m), so (B) 1-2 m is the correct choice based on the NCERT Class 10 Science guidelines on light reflection.

To succeed in the Preliminary exam, you must avoid the common traps illustrated in the other options. Option (A) 60 cm is a classic half-way trap; it represents only the distance to the mirror, not the image. Option (C) 1.4 m is the result of directional error—mistakenly adding the 40 cm to the initial 1 m instead of subtracting it. Finally, option (D) 2.0 m is the initial state trap, representing the total distance before any movement occurred. Always double-check if the question asks for the distance from the mirror or the distance from the image.