A ray of light hits a plane mirror lying across a floor 2m from the vertical wall. The angle of incidence of the ray is 40 degrees. At what point on the wall will the reflected light fall? Express the answer in terms of height from the floor.
angle of incidence (and of reflection) is measured from the normal to the surface
draw a sketch to see the right triangle to be solved
How can i express this in terms of height?
My answer is 0.99m am i correct?
h / 2m = tan(50º)
To determine the point on the wall where the reflected light will fall, we need to use the laws of reflection. The laws of reflection state that the angle of incidence is equal to the angle of reflection, and the incident ray, the reflected ray, and the normal to the surface all lie in the same plane.
Here's how we can solve the problem step by step:
Step 1: Draw a diagram
Draw a diagram to visualize the given scenario, including a line representing the floor, a vertical line representing the wall, and the ray of light hitting the plane mirror at an angle.
Step 2: Label the diagram
Label the diagram with relevant information. In this case, label the angle of incidence as 40 degrees and the distance between the mirror and the wall as 2m.
Step 3: Find the angle of reflection
Since the angle of incidence is equal to the angle of reflection, the angle of reflection is also 40 degrees.
Step 4: Use trigonometry
In order to find the point on the wall where the reflected light will fall, we can use trigonometry. We can start by finding the height from the floor to the point where the light hits the wall.
If we consider the right triangle formed by the ray of light, the wall, and the floor, the angle of incidence (40 degrees) is opposite the height we want to find, and the adjacent side of the triangle is the distance between the mirror and the wall (2m).
Using the tangent function, we can calculate:
tan(40 degrees) = height / 2m
Rearranging the equation to solve for height:
height = 2m * tan(40 degrees)
Step 5: Calculate the height
Using a calculator or trigonometric table, we can find the value of tan(40 degrees) and evaluate the equation:
height = 2m * tan(40 degrees)
This will give us the height from the floor to the point where the reflected light falls on the wall.