Two plane mirrors meet at a right angle (Fig. P24.3). An...

Two plane mirrors meet at a right angle (Fig. P24.3). An incident ray strikes the bottom mirror at point $B$ with an angle of incidence $\theta_{i}$; this ray reflects from each mirror once and strikes the screen on top at point $A$. (The screen is parallel to the bottom mirror.) Given the dimensions in Figure $\mathrm{P} 24.3,$ what is $\theta_{i} ?$

Key Concepts

Law of Reflection

This principle states that the angle of incidence is equal to the angle of reflection when a light ray strikes a reflective surface. It is crucial in determining the path of light in any mirror reflection problem, including single or multiple reflections.

Multiple Reflections

In systems where light reflects off more than one surface, each reflection follows the law of reflection. Understanding how successive reflections influence the overall light path is essential for analyzing configurations with two or more mirrors.

Method of Images

This technique simplifies complex reflection problems by replacing reflections with virtual images. It allows one to trace the straight-line path of light as if it were emanating from these virtual sources, making it easier to determine the angles and positions involved.

Geometric Optics

Geometric optics treats light as rays and employs principles such as reflection and refraction. It provides the fundamental framework for analyzing problems involving plane mirrors and helps in constructing the diagrammatic representations necessary for solving optical path problems.

Transcript

00:01 In the given problem here, these are the two plain mirrors which are meeting at right angle with each other.

00:14 This is the bottom mirror and this is the side mirror.

00:22 And then here this is the wall which is parallel to the bottom mirror.

00:32 A ray of light is striking at a point b.

00:38 On the bottom mirror, some angle of incidence which is given as theta i.

00:49 And this angle is missing the ray striking at the point b, whose distance from the junction point of the mirrors is given as 2 .5 meter.

01:04 Then the length of the another mirror is given as 2 .0 meter.

01:11 This rate will strike at the 4 .5 meter.

01:12 This rate will strike at the first mirror then at the second mirror using the concept of laws of reflection.

01:22 The angle of reflection will be equal to the angle of incidence.

01:27 Then this ray will suffer a reflection here at this mirror.

01:33 And finally, it is given that the ray is meeting at a point a here at the wall.

01:42 So if this angle is theta i, this angle will also be theta i.

01:49 Angle of reflection is equal to angle of incidence.

01:53 Now if this angle is theta i and this normal drawn at the vertical mirror will be parallel to the bottom mirror.

02:03 So using the concept of the parallel rays, these the parallel lines, these two are the parallel lines, this normal drawn at the bottom mirror and this vertical mirror, these two are the parallel.

02:18 So this ray will behave like a transversal...

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