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Now, find the angle θ4 shown in the figure (Figure 3) in terms of θ1 and…

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Question “Now, find the angle θ4 shown in the figure (Figure 3) in terms of θ1 and…”

Now, find the angle θ4 shown in the figure (Figure 3) in terms of θ1 and...

Now, find the angle θ4 shown in the figure (Figure 3)
in terms of θ1 and α.

Express your answer in degrees in terms of θ1 and
α.

Answer

Concepts and Reason

This problem is related to the law of reflection as well as the triangle rule, which refers to the summation of triangle angles.

Initially, find the relation between the angles

and

using the condition that the total angle made by the normal with the surface is equal to

. Later, use the law of reflection and equate the angles

and

. Then, we get the relation between the angles

and

. Later, use the condition that the sum of three angles of a triangle is equal to

and find a relation between

,

, and

. Later, eliminate the term

from this relation by using the relation between

and

. Then, the final equation contains the terms

,

, and

. Rearrange the equation for . This equation is the result you need.

Fundamentals

Normal is an imaginary line that is parallel to the common surface in two transparent media. Angle of incidence is the angle between the normal and the incidence ray. Angle of reflection is the angle between normal and reflected ray.

The angle of incidence and the angle of reflection are equal according to the law of reflection. In the figure,

represents the angle of incidence at first incidence and

represents the corresponding angle of reflection. The terms

,

, and

represents the three angles of the triangle which is formed by one ray and two surfaces.

Use the law of reflection and find the relation between

and

.


0 = 02


The figure shows that the angle created by the horizontal surface’s normal is

.


0, +, = 90°


Substitute

for

.


0 +0, = 90°


is the sum of the three angles in a triangle according to the rules of triangles.


0, +0, +a=180°


Use the equation

in this equation, and rearrange the equation for

.

(90° - ) +, +α = 180° θ, = 180° – (90° -4)-α = 90° +θ -α

Ans:

The expression for angle

in terms of the angle

and the angle

is

θ, = 90° +θ -α

.

Conclusion

Above is the solution for “Now, find the angle θ4 shown in the figure (Figure 3) in terms of θ1 and…“. We hope that you find a good answer and gain the knowledge about this topic of science.


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