A community science team decides to build a solar cooker that concentrates sunlight onto a cooking vessel by means of a large spherical mirror of diameter 1.0m. The design requires the solar rays to be focussed 40cm in front of the reflecting surface.
(i) Give one reason for preferring a concave mirror over a convex or plane mirror for this purpose.
(ii) Assuming sunlight to consist of parallel rays, calculate the focal length the mirror must have. State whether the required focal length is consistent with the given geometry.
(iii) The average solar power incident per unit area on Earth’s surface at noon is about 700W m−2. Estimate the total power that can be concentrated on the cooking vessel if the mirror reflects 80% of the incident radiation and the reflected rays fall on a circular spot of diameter 10cm at the focus.
(iv) Based on your calculation in part (iii), discuss briefly (two points) whether the designed cooker would be effective for boiling 1L of water at room temperature.