Difference between Look down one’s nose at something and Turn up one’s nose at something

look down one’s nose at something—treat smth. with contempt:

• Jolyon’s water-colors were on view there. He went in to look down his nose at them—it might give him some faint satisfaction.

turn up one’s nose at something — = look down one’s nose at something:

• Uncle Jeremy never turned up his nose at a bowl of bean-porridge.