Question

a window on the side of a house reflects the light from a sunset off of it at an angle of 74°. at what angle did the sunset light hit the window?

Explanation:

Identify the physical scenario

We are given a scenario where light from a sunset reflects off a window. The problem states that the light reflects off the window at an angle of \(74^\circ\). We need to find the angle at which the sunset light hit the window.

Define the angles of reflection

In optics, the behavior of light reflecting off a smooth surface is described by the Law of Reflection.

• The angle of incidence (\(\theta_i\)) is the angle between the incoming (incident) ray and the normal (perpendicular line) to the surface.
• The angle of reflection (\(\theta_r\)) is the angle between the reflected ray and the normal to the surface.

The problem states that the light reflects "at an angle of \(74^\circ\)", which represents the angle of reflection:

$$\theta_r = 74^\circ$$

Apply the Law of Reflection

The Law of Reflection states that the angle of incidence is equal to the angle of reflection:

$$\theta_i = \theta_r$$

Calculate the angle of incidence

Using the equality:

$$\theta_i = 74^\circ$$

Therefore, the angle at which the sunset light hit the window (the angle of incidence) is \(74^\circ\).

Answer:

\(74^\circ\)