Question

A reflective telescope uses a parabolic mirror to focus light rays before creating an image with the eyepiece. If the focal length (the distance from the bottom of the mirror's bowl to the focus) is 140 mm and the mirror has a 70 mm diameter (width), what is the depth of the bowl of the mirror? The distance from the bottom of the mirror's bowl to the focus is p. The vertex location is not specified (or needed), so use (0, 0) for simplicity. The equation for the mirror is a horizontal parabola (with x the distance along the telescope and y the position out from the center). $(y - 0)^2 = 4p(x - 0)$ $y^2 = 560x$ Since the diameter of the bowl of the mirror is 70 mm, the points at the rim of the mirror have y-values of 35 mm and -35 mm. The x-value of either point will be the same as the x-value of the point directly above the bottom of the bowl, which equals the depth of the bowl. Since the points on the rim lie on the parabola, use the equation of the parabola to solve for the x-value of either edge of the mirror. $35^2 = 560x$ x ? mm The bowl is approximately 2.19 mm deep.

          A reflective telescope uses a parabolic mirror to focus light rays before creating an image with the eyepiece. If the focal length (the distance from the bottom of the mirror's bowl to the focus) is 140 mm and the mirror has a 70 mm diameter (width), what is the depth of the bowl of the mirror?

The distance from the bottom of the mirror's bowl to the focus is p. The vertex location is not specified (or needed), so use (0, 0) for simplicity. The equation for the mirror is a horizontal parabola (with x the distance along the telescope and y the position out from the center).

$(y - 0)^2 = 4p(x - 0)$

$y^2 = 560x$

Since the diameter of the bowl of the mirror is 70 mm, the points at the rim of the mirror have y-values of 35 mm and -35 mm. The x-value of either point will be the same as the x-value of the point directly above the bottom of the bowl, which equals the depth of the bowl. Since the points on the rim lie on the parabola, use the equation of the parabola to solve for the x-value of either edge of the mirror.

$35^2 = 560x$

x ? mm

The bowl is approximately 2.19 mm deep.

A reflective telescope uses a parabolic mirror to focus light rays before creating an image with the eyepiece. If the focal length (the distance from the bottom of the mirror's bowl to the focus) is 140 mm and the mirror has a 70 mm diameter (width), what is the depth of the bowl of the mirror?

The distance from the bottom of the mirror's bowl to the focus is p. The vertex location is not specified (or needed), so use (0, 0) for simplicity. The equation for the mirror is a horizontal parabola (with x the distance along the telescope and y the position out from the center).

(y - 0)^2 = 4p(x - 0)

y^2 = 560x

Since the diameter of the bowl of the mirror is 70 mm, the points at the rim of the mirror have y-values of 35 mm and -35 mm. The x-value of either point will be the same as the x-value of the point directly above the bottom of the bowl, which equals the depth of the bowl. Since the points on the rim lie on the parabola, use the equation of the parabola to solve for the x-value of either edge of the mirror.

35^2 = 560x

x ? mm

The bowl is approximately 2.19 mm deep.

Added by Kimberly O.

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