While it's challenging to predict the exact technological advancements that will occur in the future, it is highly unlikely that we will be able to build a telescope capable of observing the surface of a planet in another galaxy in great detail. The distances involved and the limitations imposed by physics make such observations extremely difficult, if not impossible, with our current understanding and technology.
The scale of intergalactic distances is vast. Even the closest galaxy to our Milky Way, the Andromeda Galaxy, is about 2.5 million light-years away. This means that the light we receive from Andromeda today started its journey 2.5 million years ago. Observing the surface of a planet in Andromeda in great detail would require a telescope with an unimaginable level of sensitivity, resolution, and light-gathering power.
There are several challenges that prevent us from achieving such detailed observations:
Limitations of Light: Light from distant objects gets dimmer and more spread out as it travels through space. By the time it reaches us from another galaxy, it becomes exceedingly faint and challenging to detect. Gathering enough light to form a detailed image of a planet's surface would require an extraordinarily large and sensitive telescope.
Angular Resolution: The ability to resolve fine details in an image is limited by the diffraction of light, which depends on the diameter of the telescope's aperture. The larger the aperture, the better the angular resolution. However, building a telescope with an aperture large enough to observe planetary surfaces in distant galaxies would be an immense engineering challenge.
Atmospheric Interference: Earth's atmosphere poses a significant challenge for ground-based telescopes. It distorts and scatters incoming light, degrading the image quality. Observations from space-based telescopes are less affected by atmospheric interference, but the challenges of intergalactic observations remain substantial.
Planetary Atmospheres: Even if we could overcome the above challenges and observe a planet's surface in another galaxy, the presence of that planet's atmosphere would further complicate matters. Planetary atmospheres scatter and absorb light, making it difficult to discern surface details.
While advancements in technology and observational techniques will undoubtedly continue to enhance our ability to study distant objects, observing the surface of a planet in another galaxy in great detail is a monumental task that stretches beyond our current technological capabilities and the limits imposed by the laws of physics.