Two mirrors are placed at a 90° angle to each other. A light ray strikes one mirror 0.730 m from the intersection of the mirrors with an incident angle of 36.5°. The ray then travels a distance d before reflecting from the second mirror. (a) What is the distance d?

1.2273 m

To find the distance d traveled by the light ray before reflecting from the second mirror, we can use the law of reflection and some basic trigonometry.

Let's break down the problem step by step:

Step 1: Draw a diagram
Start by drawing a diagram to visualize the problem. Draw two intersecting lines to represent the mirrors, and label the given distances and angles.

```
|
|
| • R2
----------•------ 90°
R1 /|
/ |
/ |
/ |
/θ |
•-----
```
In this diagram, R1 represents the reflection point on the first mirror, R2 represents the reflection point on the second mirror, and θ represents the incident angle of the light ray.

Step 2: Applying the Law of Reflection
According to the law of reflection, the angle of incidence (θi) is equal to the angle of reflection (θr).

```
|
|
θi | • R2
----------•------ 90°
R1 /|
/ |
θr / |
/ |
/ |
•-----
```

Step 3: Finding the Incident and Reflection Angles
In the given problem, the incident angle θi is 36.5°. Therefore, the reflection angle θr will also be 36.5°.

```
|
|
36.5°| • R2
----------•------ 90°
R1 /|
/ |
36.5° / |
/ |
/ |
•-----
```

Step 4: Applying Trigonometry
Now, let's use basic trigonometry to find the distance d.

In the triangle formed by the incident ray, the first mirror, and the second mirror, we can use the tangent function:

tan(θ) = opposite/adjacent

Since we know the opposite side and the adjacent side, we can rewrite the equation as:

tan(90° - 36.5°) = R2/R1

tan(53.5°) = R2/0.73 m

Now, rearrange the equation to solve for R2:

R2 = tan(53.5°) * 0.73 m

Use a calculator to find the value of tan(53.5°) and then multiply it by 0.73 m to get the value of R2.

Step 5: Calculating the value of R2
Using a calculator:

tan(53.5°) ≈ 1.301

Now, multiply:

R2 = 1.301 * 0.73 m

R2 ≈ 0.949 m

Therefore, the distance d traveled by the light ray before reflecting from the second mirror is approximately 0.949 meters.