A ray of light is incident on a plane mirror at an angle 30° with the normal at the point of incidence. The ray will be deviated from its incidence direction by what angle ?

1. Nature of Light and Rectilinear Propagation (basic)

Light is a form of energy that enables us to see the world around us. In our study of Geometrical Optics, we treat light as a ray—an idealized narrow beam that represents the path along which light energy travels. The most fundamental property of light in a uniform medium is Rectilinear Propagation, which simply means that light travels in straight lines. This straight-line behavior is why we can use geometry to trace light paths and explain how images are formed Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.134.

Two critical observations support this straight-line nature: the formation of sharp shadows by opaque objects and the working of a pinhole camera. If light could easily curve around everyday objects, shadows would not have distinct edges. Furthermore, light travels at an incredible, finite speed. In a vacuum, this speed is approximately 3 × 10⁸ m s⁻¹, which is the universal speed limit Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148.

When a light ray traveling in a straight line encounters a surface like a mirror, it undergoes reflection. The ray doesn't just bounce randomly; it follows the Law of Reflection, where the angle of incidence (i) equals the angle of reflection (r). An important concept here is the Angle of Deviation (δ). This represents how much the light ray has "turned" from its original straight-line path. Since a straight line is 180°, if light hits a mirror and bounces back, the deviation is calculated as: δ = 180° - (i + r), or simply 180° - 2i.

Sources: Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.134; Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148

2. Fundamental Laws of Reflection (basic)

Concept: Fundamental Laws of Reflection

3. Characteristics of Images in Plane Mirrors (basic)

When you look into a plane mirror, the image you see isn't just a simple reflection; it follows specific geometric rules. First and foremost, the image is always virtual and erect. "Virtual" means the light rays don't actually meet at the image point—they only appear to originate from there—which is why you cannot project this image onto a screen. "Erect" simply means the image is right-side up, unlike a pinhole camera which produces upside-down images Science, class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.135. Additionally, the size of the image is exactly equal to the size of the object, a property that distinguishes plane mirrors from most curved mirrors Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.156.

One of the most fascinating aspects of plane mirrors is lateral inversion. If you raise your left hand, your image appears to raise its right hand. This left-right reversal is a signature characteristic of reflections in plane mirrors Science-Class VII, NCERT (Revised ed 2025), Light: Shadows and Reflections, p.162. Furthermore, the distance of the image from the mirror is exactly the same as the distance of the object from the mirror. If you stand 1 meter in front of a mirror, your image is 1 meter "behind" the mirror, making the total distance between you and your image 2 meters.

To understand how light behaves during this process, we look at the Angle of Deviation (δ). When a light ray hits the mirror at an angle of incidence (i), it reflects at the same angle (r = i). If the mirror weren't there, the light would have traveled in a straight line (180°). The mirror forces it to turn. The total angle by which the ray is "turned away" from its original path is calculated as δ = 180° - 2i. This geometric property is fundamental in designing optical instruments like periscopes.

Property	Description
Nature	Virtual and Erect (cannot be caught on screen).
Size	Magnification is exactly 1 (Image size = Object size).
Position	Object distance (u) = Image distance (v).
Orientation	Laterally inverted (Left becomes Right).

Sources: Science, class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.135; Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.156; Science-Class VII, NCERT (Revised ed 2025), Light: Shadows and Reflections, p.162

4. Refraction and Snell's Law (intermediate)

When light travels from one transparent medium to another, it doesn't always continue in a straight line; it bends at the interface. This phenomenon is known as refraction. The root cause of this bending is the change in the speed of light as it enters a medium of different optical density. In a vacuum, light travels at its maximum speed (approximately 3 × 10⁸ m/s), but it slows down when it enters materials like water or glass Science, Light – Reflection and Refraction, p.159. The Refractive Index (n) of a medium is a measure of this change, defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v), or n = c/v.

Refraction is governed by two fundamental laws Science, Light – Reflection and Refraction, p.148:

• First Law: The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
• Second Law (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 and a specific color of light. This is expressed as: sin i / sin r = constant. This constant is the refractive index of the second medium with respect to the first.

How the light bends depends on the relative optical densities of the two media. If light enters an optically denser medium (where it slows down), it bends towards the normal. Conversely, if it enters an optically rarer medium (where it speeds up), it bends away from the normal. For example, in a rectangular glass slab, light refracts twice—at the air-glass and glass-air interfaces—resulting in an emergent ray that is parallel to the incident ray but laterally displaced Science, Light – Reflection and Refraction, p.159.

Scenario	Speed Change	Bending Direction
Rarer to Denser (e.g., Air to Glass)	Decreases	Towards the Normal (i > r)
Denser to Rarer (e.g., Glass to Air)	Increases	Away from the Normal (i < r)

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

5. Total Internal Reflection (TIR) (exam-level)

Welcome back! Now that we have mastered the basics of refraction and Snell’s law, we arrive at one of the most fascinating phenomena in optics: Total Internal Reflection (TIR). This isn't just a textbook concept; it is the reason why diamonds sparkle and how high-speed internet reaches your home through optical fibers.

To understand TIR, we must look at what happens when light travels from an optically denser medium (like water or glass) to an optically rarer medium (like air). According to the laws of refraction, when light enters a rarer medium, it bends away from the normal Science, Light – Reflection and Refraction, p.148. As we gradually increase the angle of incidence (i), the angle of refraction (r) also increases, moving closer and closer to the interface between the two media.

Eventually, we reach a specific point called the Critical Angle. This is the angle of incidence for which the angle of refraction is exactly 90°. At this stage, the light ray "grazes" along the surface. If you increase the angle of incidence even slightly beyond this critical angle, the light can no longer refract into the second medium. Instead, it is entirely reflected back into the first (denser) medium. This is Total Internal Reflection.

Scenario	Angle of Incidence (i)	Result
Partial Refraction	i < Critical Angle	Light bends away from normal into the rarer medium.
Grazing Emergence	i = Critical Angle	Light travels along the boundary (r = 90°).
Total Internal Reflection	i > Critical Angle	Light reflects back into the denser medium.

For TIR to occur, two strict conditions must be met:

• The light must be traveling from an optically denser medium to an optically rarer medium.
• The angle of incidence must be greater than the critical angle for that pair of media.

We see this in nature and technology constantly. For instance, a diamond sparkles because its refractive index is very high (2.42), which makes its critical angle very small (about 24.4°) Science, Light – Reflection and Refraction, p.149. This causes light to be "trapped" and reflected multiple times inside before emerging. TIR is also a critical component in the formation of rainbows, alongside refraction and dispersion Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.335.

Sources: Science , Light – Reflection and Refraction, p.148; Science , Light – Reflection and Refraction, p.149; Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.335

6. Scattering and Dispersion of Light (exam-level)

Welcome to a fascinating part of optics where we move beyond simple paths of light and explore its vibrant nature. To master Dispersion and Scattering, we must first understand that what we perceive as "white light" is actually a mixture of many different colors, each possessing its own unique wavelength.

1. Dispersion of Light
Dispersion is the phenomenon where white light splits into its seven constituent colors (VIBGYOR) when passing through a medium like a glass prism. This happens because the speed of light in a medium (like glass) depends on its wavelength. While all colors travel at the same speed in a vacuum, they slow down by different amounts in glass. Red light, having a longer wavelength, travels faster and bends the least, whereas Violet light, with a shorter wavelength, travels slower and bends the most Science, The Human Eye and the Colourful World, p.167. This creates a band of colors known as a spectrum.

2. Scattering of Light
Unlike dispersion, which is about light splitting inside a medium, scattering is about light being redirected in various directions by particles in its path. In our atmosphere, molecules of air and fine dust particles are smaller than the wavelength of visible light. These particles are much more effective at scattering shorter wavelengths (blue/violet) than longer wavelengths (red). Specifically, red light has a wavelength about 1.8 times greater than blue light Science, The Human Eye and the Colourful World, p.169. This explains why the sky appears blue during the day (scattered blue light reaches our eyes) and why the sun appears reddish at sunset (the blue light is scattered away during the long path through the atmosphere, leaving the unscattered red light) FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Solar Radiation, Heat Balance and Temperature, p.68.

Feature	Dispersion	Scattering
Core Process	Splitting of white light into a spectrum.	Redirection of light by particles.
Medium Required	A refracting medium like a prism or water droplet.	A medium with suspended particles (colloids, atmosphere).
Key Factor	Difference in refractive index for different wavelengths.	Particle size relative to wavelength.

Sources: Science, The Human Eye and the Colourful World, p.167; Science, The Human Eye and the Colourful World, p.169; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Solar Radiation, Heat Balance and Temperature, p.68

7. The Geometry of Light Deviation (intermediate)

When a ray of light travels, it naturally seeks to move in a straight line. The Angle of Deviation (δ) is a geometric measure of how much a ray has been forced to "turn" from its original path due to reflection or refraction. Imagine the light ray as a car driving straight; if a mirror suddenly blocks its path, the car must steer in a new direction. The angle between where the car was going and where it ended up is the deviation.

To calculate this for a plane mirror, we rely on the Law of Reflection, which states that the angle of incidence (i) is always equal to the angle of reflection (r) Science, class X (NCERT 2025 ed.), Chapter 9, p.135. If the mirror were absent, the ray would have completed a straight line (180°). Because of the reflection, the ray is "pushed" away. Geometrically, the deviation is the total straight-line angle minus the sum of the incident and reflected angles. Thus, the formula is δ = 180° – (i + r). Since i = r, we simplify this to δ = 180° – 2i.

This concept isn't limited to mirrors. In lenses, the degree of deviation depends on the focal length — a lens with high power causes a larger deviation than one with lower power Science, class X (NCERT 2025 ed.), Chapter 9, p.157. However, there is one unique case: a ray passing through the optical centre of a thin lens suffers zero deviation and passes straight through Science, class X (NCERT 2025 ed.), Chapter 9, p.151.

Incidence Type	Angle (i)	Deviation (δ)	Physical Effect
Normal Incidence	0°	180°	Ray retraces its path back Science, Class VIII, NCERT (Revised ed 2025), Chapter 10, p.158
Glancing Incidence	90°	0°	Ray grazes the surface without turning

Sources: Science, class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.135; Science, class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.151; Science, class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.157; Science, Class VIII, NCERT (Revised ed 2025), Chapter 10: Light: Mirrors and Lenses, p.158

8. Mathematical Calculation of Deviation (δ = 180° - 2i) (exam-level)

When we study the path of light, we are often interested in how much a surface like a mirror "deflects" or changes the course of a light ray. To understand the Angle of Deviation (δ), imagine the original direction the light would have traveled if the mirror were not there. This imaginary path is a straight line extending from the point of incidence. However, the mirror reflects the ray into a new path. The angle between that original straight-line path and the actual reflected path is the deviation.

To calculate this mathematically, we rely on the fundamental Laws of Reflection. According to these laws, the angle of incidence (i) is always equal to the angle of reflection (r) Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p. 139. Geometrically, the incident ray, the normal, and the original path form a straight line, which measures 180°. The total angle occupied by the actual light rays (the incoming ray and the reflected ray) is i + r. Therefore, the deviation is simply the remaining portion of that 180° straight line:

δ = 180° - (i + r)

Since we know that i = r Science, Class VIII (NCERT 2025 ed.), Light: Mirrors and Lenses, p. 158, we can simplify this to the exam-standard formula: δ = 180° - 2i. This tells us that as the angle of incidence increases, the deviation decreases. For example, if a ray hits a mirror at an angle of 30° with the normal, the deviation is 180° - 2(30°) = 120°.

It is important to distinguish between the angle with the normal (i) and the angle with the mirror surface (often called the glancing angle, θ). Because the normal is at 90° to the mirror surface Science, Class VIII (NCERT 2025 ed.), Light: Mirrors and Lenses, p. 158, i = 90° - θ. Substituting this into our formula gives δ = 180° - 2(90° - θ), which simplifies to δ = 2θ. This is a quick shortcut: the deviation is always double the glancing angle!

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.139; Science, Class VIII (NCERT 2025 ed.), Light: Mirrors and Lenses, p.158; Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.166

9. Solving the Original PYQ (exam-level)

This question beautifully integrates the Laws of Reflection with basic geometry to test your understanding of how light changes its path. You have recently mastered the building block that the angle of incidence (i) is always equal to the angle of reflection (r), a core principle found in Science, Class X (NCERT 2025 ed.). However, the UPSC often goes one step further by asking for the angle of deviation (δ), which is the total "turn" the light ray takes compared to its original, uninterrupted straight-line path.

To arrive at the answer, visualize the incident ray continuing in a straight line as if the mirror were not there. That straight path represents a total angle of 180°. Because the ray is reflected at 30° from the normal, the total angular space occupied by the incident and reflected rays is 2i (or 60°). The angle of deviation is the remaining angle required to complete that 180° straight line. By applying the formula δ = 180° - 2i, we calculate 180° - 2(30°), which leads us directly to the correct answer (C) 120°. Always remember to measure deviation from the ray's intended path, not the mirror surface.

UPSC includes specific traps to test your precision. Option (A) 30° is a classic distractor; it is simply the angle of reflection, which students often confuse with deviation in a hurry. Option (B) 60° is the glancing angle trap or the sum of (i+r), which represents the angle between the two rays but not the change from the original direction. By distinguishing between the final position of the ray and the total change in its trajectory, you avoid these common pitfalls.