# How does special relativity affect magnification and ray tracing?

I've been trying to look for material online which explains the special relativistic case of optics and magnification, but I still remain rather confused.

One example that confuses me slightly is that if a relativistically moving lens. To simplify things, let the object be far away such that the image forms at the focal point. My gut feeling tells me that at a particular instant, the points measured between the camera and the object simultaneously in the lens's frame follow length contraction, and the image formed should be bigger.

Similarly, if instead, the object is moving relativistically, while the lens remains still, the distance between the simultaneously measured points should not be affected by any contraction whatsoever (as the frame of the lens is not moving), and the image size is the same.

Am I on the correct train of thought here, or are there some flaws with my thinking?

It is very much possible that pictures will be different but analysis seems to be quite complex.

There are the following phenomena that affect picture:

Light time correction: https://en.wikipedia.org/wiki/Light-time_correction

Aberration of light: https://en.wikipedia.org/wiki/Aberration_of_light

In the framework of SR: - Relativity of simultaneity.

Sure - relativistic length contraction.

1. If lens is “moving” in the reference frame of the object, lens contracts. Also we have to consider beams of light that RECEIVED when the lens and the object are at points of closest approach.

2. If object is “moving” in the reference frame of the lens, object contracts. Then we have to consider beams of light that were EMITTED when the object and the lens were at points of closest approach.

There are parallels with measurement of time dilation by means of the Transverse Doppler Effect: Observer will measure redshift if a source-clock is "moving" in his frame (the clock runs slower) or blueshisft (the clock runs faster) if he is "moving" in the clock's frame. Light time correction and aberration of light also affect measurements in this case.

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

It is also important to note that the observer in the lens frame can explain that picture doubly, either by ascribing himself state of rest or motion in the object’s frame.

It is very important to consider how the object was highlighted. It is also important to consider aberration of light, since it takes time for the light to reach focal point.

In the framework of Special Relativity beams that were simultaneously emitted (from the different parts of the object) in the object’s frame were not emitted simultaneously in the lens frame, and image will be distorted.

You can find some ideas how these mentioned above factors can affect picture in the papers that consider pictures by simple pinhole camera.

https://en.wikipedia.org/wiki/Terrell_rotation

https://www.researchgate.net/publication/312494874_THE_TERRELL-PENROSE_ROTATION_WHEN_PHOTOGRAPHING_A_SPHERE_AT_REST_WITH_A_MOVING_CAMERA

https://www.researchgate.net/publication/304794967_Photographing_using_relativistic_camera_-obscura