Ok, disclaimer: I am not an astronomer and this might all be rubbish. I suspect I'm neglecting relativistic effects that might be important, for example.
The NIRCAM instrument on JWST has a wavelength range of about 600 - 5000nm [1]. The human eye is sensitive to around 380nm - 700nm.
To shift blue light (380nm) down to the upper frequency range of NIRCAM (600nm) requires a redshift of:
z = Δλ / λ0 = 0.58
This is related to the velocity of the object by:
z = v / c
and the velocity is related to distance (approximately) by the Hubble constant (H0 ~ 71 km/s / Mpc):
d = v/ H0
So we can rearrange and solve for distance to get:
d = z c / H0 = 8 billion light years.
The southern ring nebula is more like 2000 light years from us, so not even vaguely far enough that NIRCAM would see "originally-visible" light. The deep field image might actually be far enough... the faintest galaxies there might be something like 12 billion light years away [2].
The NIRCAM instrument on JWST has a wavelength range of about 600 - 5000nm [1]. The human eye is sensitive to around 380nm - 700nm.
To shift blue light (380nm) down to the upper frequency range of NIRCAM (600nm) requires a redshift of:
z = Δλ / λ0 = 0.58
This is related to the velocity of the object by:
z = v / c
and the velocity is related to distance (approximately) by the Hubble constant (H0 ~ 71 km/s / Mpc):
d = v/ H0
So we can rearrange and solve for distance to get:
d = z c / H0 = 8 billion light years.
The southern ring nebula is more like 2000 light years from us, so not even vaguely far enough that NIRCAM would see "originally-visible" light. The deep field image might actually be far enough... the faintest galaxies there might be something like 12 billion light years away [2].
[1] https://www.stsci.edu/jwst/instrumentation [2] https://www.nasa.gov/content/discoveries-hubbles-deep-fields