Shapiro Time Delay

What you are seeing: a light signal traveling from an emitter to a receiver passes near a massive body (the Sun at the origin). In flat space the signal would travel in a straight line parallel to the $x$ -axis at impact parameter $b$ . In General Relativity the signal experiences a time delay $\delta t = 2M \ln(4 r_E r_R / b^2)$ relative to the flat-space expectation, where $r_E$ and $r_R$ are the emitter and receiver distances from the Sun.

The delay is logarithmic in $b$ , growing rapidly as the signal grazes the body. For light grazing the Sun, the round-trip Cassini delay was about $250$ microseconds; Bertotti, Iess and Tortora measured it to high precision in 2003 to test the PPN parameter gamma.

Figure 1. Shapiro delay. Method: closed-form PPN formula with full Schwarzschild overlay.

b (units M)20

r_E = r_R1000

speed2

WHAT TO TRY

Lower the impact parameter b toward the Sun: the logarithmic Shapiro delay grows, and the race panel shows the real photon falling further behind the flat-space reference. Grazing rays are delayed most.
Read the delta-t vs b curve: the delay diverges logarithmically as b goes to zero, which is why the classic test times radar echoes off planets passing near the solar limb.
Note this is a delay, not a bending: even a ray that travelled a straight path would arrive late, because clocks run slow deep in the Sun gravitational potential.