Suppose a reflector has a primary mirror with a diameter of 100 cm, and a secondary mirror that

step 1 In this problem, let the distance between the primary and secondary mirror is X, which is given

Suppose a reflector has a primary mirror with a diameter of...

Suppose a reflector has a primary mirror with a diameter of $100 \mathrm{cm},$ and a secondary mirror that blocks a central region with a diameter of $25 \mathrm{cm}$. What fraction of the collecting area does the secondary mirror block? What would be the diameter of a telescope with the same collecting area if no part of its area were blocked?

Key Concepts

Equivalent Telescope Diameter

This concept involves determining the diameter of a hypothetical telescope with no obstruction that would collect the same amount of light as the obstructed telescope. It requires equating the effective area of the obstructed telescope to the area of an unobstructed circular mirror and solving for the diameter, which helps in comparing telescope designs on a common basis.

Effective Aperture

After accounting for the area blocked by the secondary mirror, the effective aperture is what remains available for collecting light. It is the net light gathering area of the telescope, and it essentially determines the telescope’s observational capability after losses due to obstruction.

Collecting Area

This concept refers to the area of the telescope’s primary light?gathering element, which is usually a circular mirror. The larger the collecting area, the more light the telescope can gather, thereby improving its ability to observe faint objects. Calculating the area typically involves the formula for the area of a circle, A = ?r².

Obstruction in Telescopes

Many telescopes use a secondary mirror that is positioned in the optical path, which causes a central obstruction. This obstruction blocks a portion of the incoming light, thereby reducing the effective collecting area. Understanding how the obstruction affects light gathering is crucial for evaluating telescope performance.

Area Calculation of Circular Apertures

The calculation of the collecting area and the blocked area involves using the geometry of circles. By applying the formula A = ?r², one can determine the areas of both the primary mirror and the obstruction, and then compute the fraction of light blocked.

Transcript

Please give Ace some feedback