Light rays strike a plane mirror at an angle of α = 38.5° as shown in the figure below. What is the angle when the reflected rays are parallel to the first mirror incident ray?
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Label the two impact points A,B, and extend the rays till they intersect at C
Then in triangle ABC,
angle A = 180-2α
and since alternate interior angles are congruent, angle C = α
So, angle B = 180-(180-2α)-α = α
β = 1/2 B
Now, what is θ in terms of α?
Find that, and you can then express β in terms of α and θ
To determine the angle at which the reflected rays are parallel to the incident ray, you'll need to apply the law of reflection. According to the law of reflection, the angle of incidence (α) is equal to the angle of reflection (β), measured with respect to the normal line to the mirror.
In the given image, α is the angle between the incident light ray and the normal line, and β is the angle between the reflected light ray and the normal line. Since you're looking for the angle at which the reflected rays are parallel to the incident ray, it means that β should be equal to α (38.5°).
However, in order to find the answer, you'll need to know the relationship between α and the angle of the mirror. If the mirror is vertical (perpendicular to the ground), the normal line would be horizontal. In this case, the angle β, which is the angle between the reflected ray and the normal line, will be the same as the angle between the incident ray and the mirror. Therefore, β would be 38.5°.
However, if the mirror is inclined (not vertical), you'll need to consider the fact that the angle between the incident ray and the mirror is different from the angle between the reflected ray and the mirror. In that case, you would have to provide additional information about the angle of the mirror in order to calculate the angle at which the reflected rays are parallel to the incident ray.