Two plane mirrors are inclined at 90^∘. An object is placed between them whose coordinates are (

step 1 Hello and welcome to this video solution of numerate. Okay, so we are given two mirrors perpendi

Two plane mirrors are inclined at 90^∘. An object is placed...

Two plane mirrors are inclined at $90^{\circ}$. An object is placed between them whose coordinates are $(a, b)$. Find the position vectors of all the images formed : (Take $\ddot{\mathbf{i}}, \overrightarrow{\mathbf{j}}$ are unit vectors along $x-y$ axis) (a) $-a \hat{\mathbf{i}}-b \hat{\mathbf{j}}, a \hat{\mathbf{i}}-b \hat{\mathbf{j}},-a \hat{\mathbf{i}}+b \hat{\mathbf{j}}$(b) $-a \hat{\mathbf{i}}+b \hat{\mathbf{j}},-a \hat{\mathbf{i}}-b \hat{\mathbf{j}}, a \hat{\mathbf{i}}-b \hat{\mathbf{j}}$ (c) $a \hat{\mathbf{i}}+b \hat{\mathbf{j}},-a \hat{\mathbf{i}}-b \hat{\mathbf{j}},+a \hat{\mathbf{i}}-b \hat{\mathbf{j}}$ (d) none of the above

Two plane mirrors are inclined at $90^{\circ}$. An object is placed between them whose coordinates are $(a, b)$. Find the position vectors of all the images formed : (Take $\ddot{\mathbf{i}}, \overrightarrow{\mathbf{j}}$ are unit vectors along $x-y$ axis)
(a) $-a \hat{\mathbf{i}}-b \hat{\mathbf{j}}, a \hat{\mathbf{i}}-b \hat{\mathbf{j}},-a \hat{\mathbf{i}}+b \hat{\mathbf{j}}$(b) $-a \hat{\mathbf{i}}+b \hat{\mathbf{j}},-a \hat{\mathbf{i}}-b \hat{\mathbf{j}}, a \hat{\mathbf{i}}-b \hat{\mathbf{j}}$
(c) $a \hat{\mathbf{i}}+b \hat{\mathbf{j}},-a \hat{\mathbf{i}}-b \hat{\mathbf{j}},+a \hat{\mathbf{i}}-b \hat{\mathbf{j}}$
(d) none of the above

Key Concepts

Plane Mirror Image Formation

This concept involves understanding how plane mirrors create images by reflecting light such that the angle of incidence equals the angle of reflection. The image appears as a laterally inverted version of the object, equidistant behind the mirror as the object is in front, which is central to determining the image’s position.

Reflection Transformation in Coordinate Geometry

This concept pertains to the mathematical process of obtaining the coordinates of an image by applying reflection transformation rules. Typically, reflecting an object across a line (or mirror) in a coordinate system involves changing the sign of the coordinate perpendicular to the mirror while keeping the other coordinate constant.

Vector Representation in a Coordinate System

This concept deals with representing points and their transformations through vectors, using unit vectors along the coordinate axes. It simplifies the analysis of geometric transformations, such as reflections, by expressing positions and movements in a concise, mathematical form.

Multiple Reflections and Composite Transformations

This concept is about analyzing situations where an object undergoes more than one reflection. When mirrors are arranged at a specific angle, such as 90°, the successive reflections lead to composite transformations that must be considered in sequence to determine all the images formed.

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