Question

( 25 POINTS )There is a light pole on one bank of a small pond. You are standing up while fishing on the other bank. After reflection from the surface of the water, part of the light from the bulb at the top of the pole reaches your eyes. Use a ray diagram to help find a point on the surface of the water from where the reflected ray reaches your eyes.

Determine an expression for the distance from this point on the water to the bottom of the light pole if the height of the pole is H , your height is h , and the distance between you and the light pole is L .

You must answer in terms of these varibles.

Answer 1

To find the point on the surface of the water from where the reflected ray reaches your eyes, use the law of reflection and draw a ray diagram. The distance from this point to the bottom of the light pole can be determined using similar triangles.

Step-by-step explanation:

To find a point on the surface of the water from where the reflected ray reaches your eyes, we can use the law of reflection.

The angle of incidence (i) is equal to the angle of reflection (r).

In this case, the angle of incidence is the angle between the light ray and the normal to the surface of the water, and the angle of reflection is the angle between the reflected ray and the normal.

We can draw a ray diagram with the light pole, the point on the surface of the water, and your eyes to find the position of the point on the surface from where the reflected ray reaches your eyes.

The distance from this point to the bottom of the light pole can be determined using similar triangles.

Let's assume the distance from the point on the water to the bottom of the light pole is x. The height of the light pole is H, your height is h, and the distance between you and the light pole is L. Using similar triangles, we have:

x / H = (x+h) / L

Multiplying both sides by H and rearranging the equation gives:

x = (H * h) / (L - H)