Question

Throughout the semester your instructor has paced back and forth in front of the projection screen, introducing distortions in your perceived image of the screen due to his overwhelming gravitational field. How much is light bent by his head as it grazes his ear? (Assume the instructor’s head does not contain a black hole.)

Answer 1

From Einstein's theory of General Relativity, the deflection angle can be approximately calculated by the relation,

where m = mass of the object which is deforming the trajectory of light, d is the distance from the observer to the mass m.

Here, m = mass of the instructor's head can be approximated to be about 5kg.

d = distance from the instructor to you which can be approximated to be around 10 m

This gives the deflection angle to be approximately,

To give you an estimate of how small this angle is, consider Rayleigh's criteria for resolution.

where d = diameter of the aperture or lens required to resolve the angle. Taking the wavelength to be approximately 550 nm and the angle to be the deflection angle above, this gives,

this is how large your lens should be to resolve this deflection angle!