We are used to seeing spectacular astronomical images in the press and on the internet. This course gives an in-depth introduction to two of the most important instruments used to create these images and explore the science behind them – telescopes and spectographs.

This course is drawn from the preparatory work for the practical residential school at the Observatori Astronomic de Mallorca. The course image shows a student at work in one of the telescope domes at the Observatori.

Geometric optics is the part of Physics responsible for the study of light and the phenomena associated with it, considering that its propagation occurs through light rays.

So it is with astronomy and its elliptical orbits and with mechanics and its vectors. It is also so in the study of the properties and behaviors of light, in the field of physics that we call geometric optics.

marginal cost is a microeconomic measure that us to evaluate the extent to which the level of production of a good is sustainable in accounting, that is, to how many quantities the company plans to profit from the production of the good.

the concept of marginal cost is simple, it means the cost of producing one more item. for example, in the case of pies, the marginal cost is the cost of producing one more pie than those that have already been produced.

it is important to understand that productive activity influences marginal cost. the marginal cost of some goods can be very high, while others may be insignificant. for example, the marginal cost of producing an extra plane is very high. already the marginal cost of a water company to provide 1l more water is derisory.

in the case of pies, the cost involves the inputs, the labor and the fixed cost, which involves the fixed space of the bakery. the level of production initially has the marginal cost decreasing because there is space and manpower available. however, to produce more you have to hire more workers and buy more inputs. if physical space is limited, workers will conflict with places, inputs and their productivity will decrease, meaning there is an optimum point of production for each level of space and manpower. from this point on, the productivity of the workers will be getting smaller because of lack of space, so that the marginal cost of producing one more pie will be increasing. so, although you have not posted the chart, but if you have the answer, you can see that my explanation goes according to the marginal cost curve that will increase from the 4th pie, answer (c).