Microlensing and Weak Lensing

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Problem 1: microlensing

The microlensing occurs when a lens passes in front of a distant source. Consider the conditions of existence of such an effect and its main features.

Problem 2: optical depth

In order to describe the probability of microlensing the notion of optical depth is used. Consider its physical sense. How many sources should one observe in order to register a few events per year?

Problem 3: microlensing and dark matter

How can microlensing help to detect and characterize dark matter in a galactic halo?

Problem 4: general relation for deflection angle

Obtain the general relation for reflection angle in the lens' field, if the surface density of the lens is given.

Problem 5: deflection Jacobian

Introduce the Jacobian of the transformation from the coordinates without lensing to the coordinates after lensing. What is its physical sense?

Problem 6: mass profile reconstruction

Propose a method to reconstruct the mass distribution basing on the measured surface brightness of the images.