How does a black hole affect light photons?

Don't think about it too much- the Newtonian physics such as the equation you stated doesn't really apply because of relativistic effects.

You might know about Einstein's suggestion that the Universe isn't just 3 dimensional- he proposed the universe being a space-time 'fabric' where space and time aren't always constant. Basically, mass distorts space and time around it- and since black holes are extremely massive (as in, have a lot of mass), they distort the spacetime around them dramatically... in fact, so much so that it is impossible for light to escape that particular area of spacetime.

That's my understanding of it anyway. There's probably more to add (the light might gain mass, E=mc^2 shows that energy and mass are interchangable when you think about it, doesn't it!?) , but it certainly cannot be explained using Newtonian physics.

Are you doing Physics in school? This should get covered pretty soon if you are- don't get too concerned about it!

This answer will, I am afraid, just add to the confusion, because if I say I am correct, I am saying the other respondents are not.

Light is not affected by gravity directly. Light does not have mass. But gravity does bend space - this is the foundation of General relativity. Yes, light does have energy, and this was once called 'relativistic mass' but generally, this is no longer much used exactly because it led to this sort of confusion.

There have been experiments made in measuring a triangle that includes the sun - that is, where a distant star was selected and measurements made of the angle from two points on the earth; each along a line that passed on two sides of the sun, and there were more than 180 degrees in the triangle, an indication that space was indeed being curved by the mass of the sun, exactly because it was already clear that light, of itself, was not affected by gravity.

The intensely focused mass of a black hole is enough to distort space so that a 'straight line' in our three-space actually goes through the black hole. It is only what we see with our observations, that appears to be evidence that the light itself is bent by the mass.

This is not simple stuff, and not easy to get a conceptual grasp of. .

Your a kid right, imagine it like this, stretch a flat piece of rubber out so that it's is tight. roll a ball bearing (a photon)over it, it will travel in a straight line in a flat space. Now put a heavy bowling ball ( a star) on the rubber sheet and roll the ball bearing again so that the straight line should just pass the bowling ball. You'll see that it actually fallows a curved path across thie make shift universe. Now imaging the bowling ball mass compacted into a tiny volume (the black hole) and the curvature of space will still be present. But this imense mass is now curving the rubber about a point and the bearing, if it gets to close, will never be able to surmount this energy barrier.

Gravity bends space. In the case of a black hole thecurvature of space is so great that the light never 'escapes'. From the photon's perspective, though, it is still travelling in a straight line.

I think what your asking hasnt been addressed yet. Im sure you understand or can picture what gravity does to light right? Of course we all can but you want to know 'why' dont you.

Spacetime is the fabric of the universe, its an invisible body that we dont really know anything about apart from observing it by how bodies move in it. Light travels as energy in what we call 'photons', these are just like pulses on the fabric of spacetime right? They are not particles but ripples of energy in this fabric, its how they have wave-partical duality behaving in some instances as particals others as wave functions as im sure you read about. Scientists dont really know what photons are so lets think of them as ripples of energy like when you stretch rope and twang it, you visibly see the ripple moving as distortion energy but when it is absorbed (like when a photon hits the back of your eye) it disappears transfering its energy to whatever it hit. So dont think of photons as physical entities - think of them as pure energy traveling through spacetime which we just observe.

So imagine space as this big wobbly jelly, now with a blackhole this spacetime fabric is distorting everything around it, as light travels on this very fabric as energy it too is distorted. Now when you get inside the escape point of light, the event horizon, spacetime kind of gets ripped/torn open, everything gets sucked in to who only knows where, we can only imagine, this is why light (photons) cant escape because the fabric they travel on cant escape either.

Photons are not massless: they do not have rest mass. Travelling at the speed of light in a vacuum is only possible for a particle with zero rest mass. At this speed a photon has a finite mass, which can be calculated using E = mc², where E is the photon energy.

A photon is a discrete packet of electromagnetic radiation. Although electromagnetic radiation has wave-like properties, it only occurs in discrete packet of energy and so also has particle-like properties.

Light has energy, and it falls in a gravitational field (Equivalence principle). Gravity operates even on particles like the photon that have zero rest mass.