A flat circular mirror of radius 0.120 m is lying on the floor. Centered above the mirror, at a height of 0.830 m, is a light source. Calculate the diameter of the bright circular spot formed on the 2.90 m high ceiling by the light reflected from the mirror
I tried drawing a figure but I just cant get it to work. I need some help. It looks like it involver the mirror equation.
To solve this problem, you are correct in using the mirror equation. Here's how you can approach it:
1. Draw a diagram: Visualize the situation. Draw a horizontal line to represent the floor, and a vertical line to represent the ceiling. Mark the mirror as a circle on the floor, and the light source above it.
2. Identify relevant quantities: Note the given information: radius of the mirror (r = 0.120 m), height of the light source (h = 0.830 m), and height of the ceiling (H = 2.90 m).
3. Apply the mirror equation: The mirror equation for a spherical mirror is given as:
1/f = 1/v + 1/u
where f is the focal length, v is the image distance, and u is the object distance. In this case, since the mirror is flat (negligible focal length), the equation simplifies to:
1/v = 1/u
4. Determine the object distance: The object distance (u) is the distance between the mirror and the light source. In this case, it is equal to the height of the light source (h = 0.830 m).
5. Solve for the image distance: Using the equation from step 4, we have:
1/v = 1/u
1/v = 1/0.830 m
6. Calculate the image distance: Flip both sides of the equation and solve for v:
v = 0.830 m
7. Determine the diameter of the image: The diameter of the bright circular spot formed on the ceiling is twice the radius of the mirror (2r). Since the image appears the same size as the object (mirror), its diameter will also be 2r.
Diameter of image = 2 × 0.120 m = 0.240 m
Therefore, the diameter of the bright circular spot formed on the ceiling is 0.240 m.
Remember, drawing a diagram can often help visualize the problem and make it easier to understand.