looked at

We need at, but we could leave out up, though I wouldn't.

Rover

vsureshThen I thought it is perhaps we want to show where exactly he was looking. Am I correct?

You could say that. At is needed because without it, sky is an incompatible direct object. You can look up a company's phone number, but you can't look up a sky. Also, we know the sky is upward, so up can be safely discarded.

She lo

Thank you Rover and Aspara Gus.
Hi Aspara Gus, please tell me what you mean by incompatible direct object.

Suresh

vsureshHi Aspara Gus, please tell me what you mean by incompatible direct object.

I just mean that if you drop at, the verb or phrasal verb look or look up becomes (or at least appears to become) transitive, meaning it uses a direct object. What I mean by incompatible object is that sky does not work as the verb

Thank you Aspara Gus

I have a doubt.
Please help me.
I look at the picture.
I look the picture. ?
My question: Though I know the second one is incorrect, I want to know what at does to the meaning here.

vsureshI want to know what at does to the meaning here.

It shows that you are directing your eyes at the picture.

Thank you Aspara Gus.