An observer is sitting 20 cm away from a circular convex mirror, with his eyes on the axis of t

step 1 An observer is setting 20 cm away from a circular convex mirror with his eyes on the axis of mir

An observer is sitting 20 cm away from a circular convex...

An observer is sitting $20 \mathrm{~cm}$ away from a circular convex mirror, with his eyes on the axis of the mirror. The mirror has diameter of $6 \mathrm{~cm}$ and focal length $30 \mathrm{~cm}$ is fixed with its principal axis horizontal. The image is formed at distance $12 \mathrm{~cm}$ from the mirror and the distance of mid-point of diameter from the pole is $0.75 \mathrm{~cm}$. The angular field of view in the horizontal plane seen in the mirror by the observer is : (a) $\tan \theta=0.5672$ (b) $\tan =0.3014$ (c) $\tan \theta=0.5279$ (d) $\tan \theta=0.2516$

An observer is sitting $20 \mathrm{~cm}$ away from a circular convex mirror, with his eyes on the axis of the mirror. The mirror has diameter of $6 \mathrm{~cm}$ and focal length $30 \mathrm{~cm}$ is fixed with its principal axis horizontal. The image is formed at distance $12 \mathrm{~cm}$ from the mirror and the distance of mid-point of diameter from the pole is $0.75 \mathrm{~cm}$. The angular field of view in the horizontal plane seen in the mirror by the observer is :
(a) $\tan \theta=0.5672$
(b) $\tan =0.3014$
(c) $\tan \theta=0.5279$
(d) $\tan \theta=0.2516$

Key Concepts

Convex Mirror

A convex mirror is a curved mirror with a reflective surface that bulges outward. It always forms virtual, upright, and diminished images irrespective of the object’s distance from the mirror. This property makes convex mirrors useful in applications like security and vehicle side mirrors where a wider field of view is desired.

Angular Field of View

Angular field of view refers to the angular extent of the observable world that is seen at any given moment through an optical instrument or reflection. In the context of mirrors, it is defined by how much of the scene in front of the mirror is captured within its curved surface, and it is determined by the geometry of the mirror and the position of the observer's eye relative to the mirror.

Mirror Equation

The mirror equation, which relates the object distance, image distance, and the focal length of a mirror, is central to understanding image formation. For a convex mirror, this equation helps in determining the virtual image position and the magnification, thereby linking the properties of the mirror to the observable characteristics like size and field of view.

Principal Axis and Pole

The principal axis is a line that passes through the center of curvature and the pole (the vertex) of the mirror; it serves as a reference line for measuring distances and angles in mirror geometry. Understanding the location of the pole and the orientation of the principal axis is essential for analyzing how an image is formed and for determining the angular field of view from the observer’s perspective.

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