The focus of a parabolic mirror is at a distance of 8cm from the center the mirror is 25cm deep find the diameter of the mirror.
To find the diameter of the mirror, we need to understand the properties of a parabolic mirror and its focal length.
First, let's determine the focal length of the mirror. The focal length is the distance from the mirror's surface to its focus point. In this case, the focal length is given as 8 cm.
The depth of the mirror, also known as the height of the mirror (h), is given as 25 cm.
In a parabolic mirror, the focal length (f) is related to the depth of the mirror (h) by the equation:
f = (1/4) * h
Plugging in the given values:
f = (1/4) * 25
f = 6.25 cm
Now, let's find the diameter of the mirror. The diameter of a parabolic mirror is related to its height by the equation:
diameter = 4 * focal length
Plugging in the value of the focal length:
diameter = 4 * 6.25
diameter = 25 cm
Therefore, the diameter of the mirror is 25 cm.
x^2 = 4py, so
x^2 = 32y
at y=25, x^2 = 800, so x = 20√2 = 28.28
That's the radius, so the diameter is 56.56 cm