In a periscope, the two plane mirrors are kept

1. Basics of Light and Rectilinear Propagation (basic)

Welcome to your first step in mastering Geometrical Optics! To understand how mirrors, lenses, and even our own eyes work, we must first understand the fundamental nature of light. Light is a form of energy that enables us to see the world around us. We perceive objects because they either emit their own light, like the Sun and stars, or reflect light falling on them. The Sun is our primary natural source of light, though humans have developed various artificial sources over millennia—from primitive fires to modern electric bulbs Science-Class VII, Chapter 11, p.154.

One of the most critical concepts in optics is the rectilinear propagation of light. This is a fancy way of saying that light travels in straight lines. Think about a beam from a flashlight or the rays of sunlight filtering through a dark forest; they don't curve or bend around objects on their own. This straight-line path is why we see sharp shadows when an opaque object blocks the light Science, Class X, Chapter: Light – Reflection and Refraction, p.134. In geometrical optics, we represent this straight-line path as a ray, which is an idealized narrow beam of light.

Finally, it is important to know that light is the fastest traveler in the universe. It moves at a staggering speed of approximately 3 × 10⁸ m/s in a vacuum Science, Class X, Chapter: Light – Reflection and Refraction, p.148. While light always seeks the most efficient path, its speed can vary slightly depending on the medium it travels through (like air, water, or glass), a property that leads to fascinating phenomena like refraction, which we will explore in later hops.

Property	Description
Propagation	Moves in straight lines (Rectilinear) in a uniform medium.
Speed (Vacuum)	Fastest possible speed: 3 × 10⁸ meters per second.
Nature	An electromagnetic wave that does not require a medium to travel.

Sources: Science-Class VII, Chapter 11: Light: Shadows and Reflections, p.154; Science, Class X, Light – Reflection and Refraction, p.134; Science, Class X, Light – Reflection and Refraction, p.148

2. Laws of Reflection and Plane Mirrors (basic)

When light hits a polished surface like a mirror, it doesn't just scatter; it bounces back in a predictable way known as Reflection. To understand this, we use two fundamental rules called the Laws of Reflection. First, the angle of incidence (the angle the incoming ray makes with an imaginary line perpendicular to the surface called the normal) is always equal to the angle of reflection (the angle the bouncing ray makes with that same normal). Second, 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.), Chapter: Light – Reflection and Refraction, p.135. Interestingly, these laws are universal—they apply to every reflecting surface, whether it is a flat plane mirror or a curved spherical mirror Science, Class VIII NCERT(Revised ed 2025), Chapter 10: Light: Mirrors and Lenses, p.160.

Images formed by a plane mirror have very specific characteristics that we rely on daily. The image is always virtual (it exists "inside" the mirror and cannot be projected onto a screen) and erect (upright). Crucially, the size of the image is exactly equal to the size of the object, and it appears to be at the same distance behind the mirror as the object is in front of it Science, class X (NCERT 2025 ed.), Chapter: Light – Reflection and Refraction, p.135. One unique feature you may have noticed is lateral inversion, where the left side of the object appears as the right side of the image.

We can use these principles to create ingenious tools like the periscope. Often used in submarines or bunkers to see over obstacles, a periscope uses two plane mirrors placed parallel to each other. Each mirror is fixed at a 45° angle to the path of light. When light strikes the first mirror, it reflects at a 90° angle down the tube. It then hits the second mirror and reflects another 90° into the observer's eye, allowing them to see objects not in their direct line of sight Science-Class VII NCERT(Revised ed 2025), Chapter 11: Light: Shadows and Reflections, p.164.

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.160; Science-Class VII NCERT(Revised ed 2025), Light: Shadows and Reflections, p.164

3. Characteristics of Images in Plane Mirrors (basic)

When you look into a plane mirror (a flat mirror), the image you see isn't just a simple copy; it follows strict geometric rules. First and foremost, the image is always virtual and erect. Unlike a 'real' image which can be caught on a screen, a virtual image only appears to be behind the mirror. Furthermore, a plane mirror always forms an image of the same size as the object, regardless of how far away you stand Science, Class VIII (NCERT), Mirrors and Lenses, p.156.

One of the most fascinating aspects is the distance relationship. If you stand 2 meters in front of a mirror, your image appears exactly 2 meters 'inside' the mirror. This means the total distance between you and your image would be 4 meters. As you move closer or further away, your image moves in perfect sync to maintain this equidistant relationship Science-Class VII (NCERT), Shadows and Reflections, p.162.

Finally, we encounter lateral inversion. This is the perceived left-right reversal where your left arm appears as the right arm of your image. This is why the word 'AMBULANCE' is written in reverse on vehicles—so drivers ahead can read it correctly in their rearview mirrors. Interestingly, letters with vertical symmetry, like 'A', 'H', 'M', 'T', or 'O', appear identical even after lateral inversion Science-Class VII (NCERT), Shadows and Reflections, p.167.

Feature	Characteristic in Plane Mirror
Nature	Virtual and Erect (upright)
Size	Same as the object (Magnification = 1)
Position	Object distance = Image distance from the mirror
Orientation	Laterally inverted (Left becomes Right)

Sources: Science, Class VIII (NCERT), Mirrors and Lenses, p.156; Science-Class VII (NCERT), Shadows and Reflections, p.162; Science-Class VII (NCERT), Shadows and Reflections, p.167

4. Spherical Mirrors: Concave and Convex (intermediate)

To understand spherical mirrors, imagine a hollow glass sphere. If you cut a piece from this sphere and silver one side, you create a mirror with a curved reflecting surface. These are broadly classified into two types based on which side is polished. A Concave Mirror has its reflecting surface curved inwards, facing toward the center of the original sphere. In contrast, a Convex Mirror has a reflecting surface that bulges outwards Science, Class X, Chapter: Light – Reflection and Refraction, p.135. A common household example is a stainless steel spoon: the side you eat from acts as a concave mirror, while the back side acts as a convex mirror. While the shape is curved, the fundamental laws of reflection still apply at every single point on the surface. However, because the surface normal (the perpendicular line) changes direction along the curve, parallel rays of light behave differently upon hitting these mirrors Science, Class VIII, Chapter: Light: Mirrors and Lenses, p.160. Concave mirrors are known as converging mirrors because they reflect parallel rays toward a single point called the Principal Focus (F). Convex mirrors are diverging mirrors because they spread rays apart, making them appear to originate from a focus point behind the mirror surface.

Feature	Concave Mirror	Convex Mirror
Reflecting Surface	Curved Inwards	Bulged Outwards
Nature of Light Rays	Converging	Diverging
Image Characteristics	Can be Real or Virtual; Magnified or Diminished	Always Virtual, Erect, and Diminished
Common Use	Shaving mirrors, Solar furnaces	Rear-view mirrors in vehicles

Understanding the geometry is key: the distance from the Pole (P) (the center of the mirror) to the Center of Curvature (C) is the Radius (R). A vital relationship to remember for intermediate optics is that the focal length (f) is exactly half of the radius of curvature: f = R/2. No matter how far an object is placed, a convex mirror will always produce an image that is smaller than the object and upright, which is why they are so reliable for wide-angle surveillance Science, Class X, p.160.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.135, 160; Science, Class VIII (NCERT 2025 ed.), Light: Mirrors and Lenses, p.160

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

Hello! Today, we explore how light behaves when it crosses boundaries between different materials. When a ray of light travels from one transparent medium to another, it usually changes direction at the interface. This bending of light is called Refraction. It occurs because light travels at different speeds in different media. The degree of bending is governed by the Refractive Index (n), defined as the ratio of the speed of light in a vacuum to the speed of light in that medium (n = c/v). According to 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: Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148.

As light moves from an optically denser medium (like water or glass) to an optically rarer medium (like air), it bends away from the normal. As we increase the angle of incidence, the angle of refraction also increases until it reaches 90°. The specific angle of incidence that results in a 90° refraction angle is known as the Critical Angle. If you increase the incident angle any further, the light can no longer pass into the second medium; instead, it is entirely reflected back into the first medium. This fascinating phenomenon is called Total Internal Reflection (TIR).

Condition	Refraction	Total Internal Reflection (TIR)
Direction	Light enters the second medium.	Light stays in the first medium.
Media Path	Rarer to Denser OR Denser to Rarer.	ONLY Denser to Rarer.
Angle Requirement	Angle of incidence < Critical angle.	Angle of incidence > Critical angle.

Understanding TIR is crucial because it is the principle behind optical fibers, which power our modern internet, and the brilliant sparkling of diamonds. While a simple periscope uses plane mirrors to reflect light, advanced periscopes often use prisms to exploit TIR, as it provides nearly 100% reflection with no loss of intensity, unlike ordinary mirrors Science, Class VII (NCERT 2025 ed.), Light: Shadows and Reflections, p.164. Interestingly, an optically denser medium (like kerosene) might have a higher refractive index than water, even if it is physically less dense (it floats on water) Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.149.

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 VII (NCERT 2025 ed.), Light: Shadows and Reflections, p.164

6. Multiple Reflection and Its Applications (intermediate)

While a single plane mirror produces just one image of an object, placing two or more mirrors together leads to the fascinating phenomenon of multiple reflection. This occurs because the image formed by the first mirror acts as a 'virtual object' for the second mirror, which then creates another image. This process can continue, producing a series of images depending on how the mirrors are positioned relative to one another Science-Class VII, Chapter 11, p. 168.

One of the most vital applications of this principle is the Periscope. Used extensively in submarines, tanks, and bunkers, a periscope allows an observer to see objects that are not in their direct line of sight. It consists of a tube with two plane mirrors placed parallel to each other. To function correctly, each mirror is inclined at an angle of 45°. When light from a distant object strikes the first mirror, it reflects at a 90° angle (following the laws of reflection where the angle of incidence equals the angle of reflection) and travels down the tube. It then hits the second mirror and reflects another 90°, finally reaching the observer's eye Science-Class VII, Chapter 11, p. 164. This clever use of multiple reflection ensures the final image remains erect (upright).

The number of images formed by two mirrors depends specifically on the angle between them. For instance, in a kaleidoscope, mirrors are usually kept at an angle (like 60°) to create beautiful, symmetrical patterns through repeated reflections of colored glass. Theoretically, if two mirrors are placed perfectly parallel to each other, they can produce an infinite number of images, as the light bounces back and forth between them indefinitely.

Sources: Science-Class VII . NCERT(Revised ed 2025), Chapter 11: Light: Shadows and Reflections, p.164, 168

7. The Geometry and Mechanism of a Periscope (intermediate)

A periscope is an ingenious optical instrument that allows an observer to see objects that are not in their direct line of sight—essentially allowing you to "see around corners" or over obstacles. Its mechanism is a practical application of the Laws of Reflection, where the angle of incidence equals the angle of reflection Science, Class X, Chapter 9, p.139. While modern military periscopes use complex prisms and lenses, the fundamental geometry remains the same as a simple tube with two mirrors.

The core geometry involves two plane mirrors placed parallel to each other at opposite ends of a tube (often a Z-shaped or rectangular box). To function correctly, each mirror is inclined at an angle of 45° to the path of the incoming light. When light from an object strikes the first mirror at this 45° angle, it is reflected at an equal angle of 45° relative to the normal (the imaginary line perpendicular to the mirror surface) Science, Class VIII, Chapter 10, p.166. This results in a total 90° change in the light's direction, sending it straight down the tube.

The light then travels to the second mirror, which is positioned parallel to the first. It undergoes another 90° reflection, directing the light toward the observer's eye. This dual-reflection setup is critical: while a single mirror would produce a laterally inverted image, the second reflection "re-flips" the image, ensuring that the observer sees an erect (upright) image of the object Science-Class VII, Chapter 11, p.164. This makes periscopes indispensable in submarines to see above the water's surface, in tanks for navigation, and for soldiers to observe from bunkers without exposing themselves to danger.

Sources: Science-Class VII . NCERT(Revised ed 2025), Chapter 11: Light: Shadows and Reflections, p.164; Science, Class VIII . NCERT(Revised ed 2025), Chapter 10: Light: Mirrors and Lenses, p.166; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.139

8. Solving the Original PYQ (exam-level)

This question bridges the gap between the fundamental Laws of Reflection you just studied and their practical application in optical engineering. To solve this, you must apply the principle that the angle of incidence equals the angle of reflection. In a periscope, the goal is to shift the line of sight vertically while keeping the final image erect and undistorted. By placing two plane mirrors in a "Z" configuration, we use two successive 90-degree reflections to redirect light from an object above the line of sight directly into the observer's eye.

As a coach, I want you to visualize the light path: the incoming ray strikes the first mirror at a 45-degree angle of incidence, reflecting at 45 degrees to travel vertically down the tube. To bring that light back to a horizontal path toward your eye, the second mirror must reverse this shift exactly. This is only possible if the mirrors are Parallel to each other. While each individual mirror is indeed tilted at an angle of 45° relative to the frame of the tube to achieve that 90-degree turn, their relationship to one another must be parallel to ensure the light exits in the same direction it entered. This geometry is beautifully explained in Science-Class VII, NCERT (Revised ed 2025), Chapter 11: Light: Shadows and Reflections.

UPSC examiners often include distractors like Option (D) 45° because they know students remember the number "45" from their textbooks. However, 45° refers to the mirror's inclination to the horizontal axis, not the angle between the two mirrors. If the mirrors were Perpendicular (Option B) or at 60° (Option C), the light would either be reflected back out of the tube or hit the side walls, failing to reach the observer. Always distinguish between the orientation of a single component and the relationship between the pair.