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Kyle lays a mirror flat on the floor and aims a laser at the mirror. The laser beam reflects off the mirror and strikes an adjacent wall. The plane of the incident and reflected beams is perpendicular to the wall. The beam from the laser strikes the mirror at a distance ????=55.9 cm from the wall. The reflected beam strikes the wall at a height ????=38.9 cm above the surface of the mirror. Find the angle of incidence thetai at which the laser beam strikes the mirror.

Respuesta :

Answer:

θr = 55.2 °

Explanation:

The law of reflection states that the angle of incidence and the angles of reflection is the same.

Let's use trigonometry to find the angle between the reflected ray, where the horizontal distance x = 55.9 cm and the vertical distance is y = 38.9 cm

    tan θ = y / x

    tan θ = 38.9 / 55.9

    θ = tan⁻¹ (0.6959)

    θ = 34.8°

This angle is measured with respect to the x-axis (horizontal), but in general the angles in optics are measured from the y-axis so that the angle is

    θ = 90 - 34.8

    θr = 55.2 °

The angle of incidence at which the laser beam strikes the mirror is 55.2°.

How to calculate the angle of incidence?

Based on the information given, trigonometry will be used to find the angle that's reflected.

Let the angle be y

Tan y = 38.9/55.9

Tan y = 0.6959

y = 34.8°

Therefore, the angle of incidence at which the laser beam strikes the mirror will be:

= 90° - 34.8°

= 55.2°

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