The focus of a parabolic mirror is at a distance of 6 cm from its vertex. If the mirror is 20 cm deep, find its diameter.
Given: The focus of a parabolic mirror is at a distance of 6 cm from its vertex. And the mirror is 20 cm deep.
Need to find: Diameter of the mirror.
Here O is the vertex and A is the Focus. So, OA = a = 6 cm.
OD is the deep of the mirror = 20 cm
BC is the diameter of the mirror.
Equation of the parabola is, y2 = 4ax
⇒ y2 = 24x
The mirror is 20 cm deep. That means the x-coordinate of the points B, C and D is 20
Both the points, B and C are on the parabola. Hence, the points satisfies the equation of the parabola.
Therefore, y2 = 24 x 20 = 480
⇒ y = 21.9
So, the coordinate of B is (20, 21.9) and the coordinate of C is (20, -21.9).
Therefore, the diameter of the mirror is = (21.9 + 21.9) cm
= 43.8 cm
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