Two mirrors are placed at a 90° angle to each other. A light ray strikes one mirror 0.620 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? answer should be in meters.
To find the distance d that the light ray travels before reflecting from the second mirror, we can use the concept of reflection and the law of reflection.
When a light ray reflects off a mirror, the angle of incidence (i) is equal to the angle of reflection (r) with respect to the normal line (the line perpendicular to the surface of the mirror). In this case, the angle of incidence is given as 36.5°.
Since the two mirrors are placed at a 90° angle to each other, the first mirror reflects the light ray by 180° - 90° = 90°, resulting in a new direction of the light ray.
To find the distance d, we need to use trigonometry. Let's consider a right triangle formed by the incident ray, the line connecting the point of incidence to the intersection of the mirrors, and the line connecting the point of incidence to the second mirror.
In this right triangle, the angle opposite to the incident ray is the reflection angle, which is 90°. The side of the triangle opposite to the angle of reflection (r) is the distance d we are trying to find.
We can use the tangent function to relate the angle of reflection to the distance d:
tan(r) = opposite / adjacent = d / distance to the first mirror
The distance to the first mirror is given as 0.620 m. Rearranging the equation:
d = tan(r) * distance to the first mirror
Calculating:
d = tan(90°) * 0.620 m
Since tan(90°) is undefined, we cannot directly use this formula for calculating d.
However, we know that the angle of reflection (r) is always equal to the angle of incidence (i) when light reflects off a mirror. Therefore, we can substitute the angle of incidence into the formula:
d = tan(i) * distance to the first mirror
Calculating:
d = tan(36.5°) * 0.620 m
Using a scientific calculator to find the tangent of 36.5°:
tan(36.5°) ≈ 0.7508
Now, substitute the values into the formula:
d = 0.7508 * 0.620 m
Calculating:
d ≈ 0.4656 m
Therefore, the distance that the light ray travels before reflecting from the second mirror is approximately 0.4656 meters.