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If the light strikes the first mirror at an angle θ1, what is the reflected angle θ2?
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The property of reflection is of light rays in which an incident light ray of the first medium is reflected onto on the surfaces of the other medium, and is returned to the original medium. The angle formed by the incident ray in relation to its normal towards the surface the same as the angle created by the reflection light that is reflected with the normal. There is no loss in intensity of light when the surface is completely reflective. Reflection of light can be explained by looking at light as matter and waves both. The light that is reflected from the incident and the surface’s normal are in one plane.♦ Relevant knowledge
This problem was solved by the Laws of reflection and basic geometric properties of triangle.
To obtain the angle required by light rays, use the basic geometric properties of triangles and Laws of reflection.
The laws of Reflection.
1. The normal rays and the reflected should both be in the same plane.
2. Only mirrors and water surfaces reflect the light rays.
3. If a light ray strikes a mirror surface, the incident angle and reflected angles of the light are equal.
These are the basic geometric properties for triangles:
* 180° is the sum of all angles in a triangle
* The sum of all the lengths of any two sides in a triangle is greater that the length on the third side.
This is the reflected ray diagram:
Figure (1)
Figure (1) shows that the angle between strike’s ray and the normal line on the first mirror, as well as the angle between reflected ray and the normal line is equal. Hence, θ1 = θ2
Angle θ3 from the simple geometry property is as follows:
θ3 = 90∘–θ2
Angle θ4 from the properties of triangle is as follows:
θ4 = 180∘–α–(90–θ1)
As shown below, the angle between the reflected ray and the normal line is equal.
θ5 = 90∘–(180∘–α–(90–θ1))
Angle θ2 is as follows:
θ1 = θ2
Ans:
The incident angle and the reflected angle are equal.
This problem was solved by the Laws of reflection and basic geometric properties of triangle.
To obtain the angle required by light rays, use the basic geometric properties of triangles and Laws of reflection.
The laws of Reflection.
1. The normal rays and the reflected should both be in the same plane.
2. Only mirrors and water surfaces reflect the light rays.
3. If a light ray strikes a mirror surface, the incident angle and reflected angles of the light are equal.
These are the basic geometric properties for triangles:
* [katex]180^\circ[/katex] is the sum of all angles in a triangle
* The sum of all the lengths of any two sides in a triangle is greater that the length on the third side.
This is the reflected ray diagram:
Figure (1)
Figure (1) shows that the angle between strike’s ray and the normal line on the first mirror, as well as the angle between reflected ray and the normal line is equal. Hence, [katex]{\theta _1} = {\theta _2}[/katex]
Angle [katex]{\theta _3}[/katex]
[katex]{\theta _3} = 90^\circ – {\theta _2}[/katex]
Angle [katex]{\theta _4}[/katex]
[katex]{\theta _4} = 180^\circ – \alpha – \left( {90 – {\theta _1}} \right)[/katex]
As shown below, the angle between the reflected ray and the normal line is equal.
[katex]{\theta _5} = 90^\circ – \left( {180^\circ – \alpha – \left( {90 – {\theta _1}} \right)} \right)[/katex]
Angle [katex]{\theta _2}[/katex]
[katex]{\theta _1} = {\theta _2}[/katex]Ans:
The incident angle and the reflected angle are equal.