A point source of light B is placed at a distance L in front of Centre of a mirror of width 'd' hung

Описание: a point source of light B is placed at a distance L in front of Centre of a mirror of width 'd' hung vertically on a wall. a man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown in figure the greatest distance over which he can see the image of the light source in the mirror is
(a) d/2 (b) d (c) 2d (d) 3d

Video Title: JEE Advanced PYQ: Unveiling the Field of View in a Plane Mirror! 💡 Pure Optics Theory!

Description:

Greetings, astute JEE Advanced aspirants! 🚀 Welcome back to Physics Behind Everything! Today, we're embarking on a conceptual exploration of a fascinating problem from a previous year's JEE Advanced exam that delves into the realm of image formation by a plane mirror and the resulting field of view for an observer. Our focus will be purely on understanding the theoretical geometry and the conceptual principles that dictate the extent to which an image is visible, without resorting to numerical calculations or intricate ray diagrams with specific measurements. Let's unravel the elegant theoretical framework governing the visibility of images in mirrors! ⚛️

Imagine a point source of light emanating its rays in all directions. Now, picture a plane mirror, a flat reflective surface, positioned in the path of some of these light rays. According to the fundamental laws of reflection, these rays will bounce off the mirror's surface, appearing to originate from a virtual image located behind the mirror. The position and characteristics of this virtual image are determined solely by the position of the object and the orientation of the mirror – a purely geometrical relationship. 📖

Now, introduce an observer, a person situated at a certain distance from the mirror. This observer can only see the image of the light source if the reflected rays from the mirror, which appear to originate from the virtual image, actually reach their eyes. The region in space from which these reflected rays can reach the observer's eyes defines the observer's field of view for that particular image. Our conceptual challenge is to understand how the size of the mirror and the relative positions of the light source, the mirror, and the observer theoretically determine the greatest distance over which the observer can perceive the image.

Consider the extreme rays of light emanating from the point source that strike the edges of the mirror. Upon reflection, these extreme rays will define the boundaries of the region from which the virtual image is visible to an observer at a certain location. The size of the mirror effectively acts as an aperture, limiting the extent of the reflected light that can reach the observer.

Conceptualizing the Geometry of the Field of View:

Imagine lines drawn from the edges of the mirror to the location of the virtual image (which is located behind the mirror at a distance equal to the object's distance in front). Now, consider the paths these reflected rays take as they travel towards the observer. The region intercepted by these extreme reflected rays at the observer's location defines the extent of the field of view.

In this specific JEE Advanced problem, the light source is at a distance L in front of the mirror, and the observer walks parallel to the mirror at a distance 2L from it. The mirror has a width d. Conceptually, the virtual image of the light source will be located at a distance L behind the mirror.

Consider the rays from the light source that strike the two opposite edges of the mirror (the top and bottom edges, considering the vertical orientation). After reflection, these rays will diverge, appearing to originate from the virtual image. The angle of divergence of these reflected rays is determined by the size of the mirror and the distance of the virtual image from the mirror.

The correct answer being (d) 3d implies a specific geometrical relationship arising from the distances L and 2L. Conceptually, the field of view extends beyond the simple projection of the mirror's width due to the divergence of the reflected rays originating from the virtual image. The distances play a crucial role in this conceptual magnification of the visible region.

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Tags: #JEEAdvancedPhysics #Optics #Reflection #PlaneMirror #FieldOfView #ConceptualPhysics #PhysicsTheory #JEE2025 #IITJEE #AdvancedConcepts #PhysicsExplained #PhysicsBehindEverything #JEEStudy #RayOptics #ImageFormation #Visibility

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