Calculate Two plane mirrors are placed with an angle of 60^∘ between them, as shown in Figure 16

Calculate Two plane mirrors are placed with an angle of 60^∘...

Calculate Two plane mirrors are placed with an angle of $60^{\circ}$ between them, as shown in Figure $16.18$.
A horizontal ray of light strikes the slanted mirror. After the ray reflects from both mirrors, what angle $\theta$ does it make with the horizontal?
A Figure $16.18$

Key Concepts

Law of Reflection

This principle states that when a ray of light strikes a reflective surface, the angle at which it hits the surface (the angle of incidence) is equal to the angle at which it leaves (the angle of reflection). This basic rule is fundamental when analyzing and predicting the path of reflected light rays in any mirror system.

Plane Mirror Geometry

Plane mirrors reflect light in such a way that the incident and reflected rays lie in the same plane. The geometry of plane mirrors involves understanding parallel ray propagation, maintaining the angles relative to the normal, and accurately applying the law of reflection to determine the subsequent ray trajectory.

Multiple Reflections

When light reflects off more than one mirror, each reflection must be analyzed in sequence using the law of reflection. The overall effect can result in a net rotation or change in the direction of the ray depending on the angles between the mirrors. This concept is particularly useful in optical systems where the orientation of multiple reflective surfaces generates predictable transformations of the incident light path.

Angle Between Mirrors

The angle separating two mirrors plays a crucial role in determining the path and final orientation of a reflected ray. The relative geometry of the mirrors affects how the successive reflections combine, typically resulting in a net change in the ray's direction that is related to the mirror angle. Understanding this concept is key to solving problems where the cumulative effect of reflections is considered.

Transcript

00:03 So this question gives us a chance to practice using the law of reflection along with some simple geometry.

00:11 Here is the situation.

00:13 We have a mirror that is inclined at an angle of 60 degrees from the horizontal, so it goes up something like this.

00:22 And then we have a light ray which is coming in at the horizontal.

00:31 So that light ray would be coming in like this.

00:34 It's a different color for the light ray.

00:42 And when the light ray reflects down, well let's figure out what that's going to look like first because there's another mirror on the horizontal down below it.

00:51 But let's just figure out what this reflection is going to look like here.

00:54 What we need to do is draw the normal line to the mirror, the first mirror.

01:06 The normal lines look like this.

01:08 It should be perpendicular to it, which means it's going up at an angle of 30 degrees.

01:14 So here's my normal line.

01:25 And if this is 90 degrees between the mirror and the normal line, that's what i've tried to define it as, and we know this angle in here is 60 degrees, and we know this angle in here must be 30 degrees.

01:48 So now according to the law of reflection, the angle of incidence should equal the angle of reflection.

01:53 Well with this mirror, the angle of incidence with this normal line was 30 degrees.

02:03 And so the outgoing angle should also be 30 degrees, which would be this.

02:20 So the incoming angle is 30 degrees.

02:22 This one should also be then 30 degrees by the law of reflection.

02:28 That means that this entire angle from the horizontal to the .....

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