I would take out some examples of famous personalities who wore glasses and later succeeded in life. For example, Stephen Hawking. Then I would tell that these days wearing spectacles has become a new fashion.
P.S. If your friend is a fashion-lover, you can add this.
If you wear glasses you would do your things much better than before. It doesn't matter if you sit continuously for three hours in front of the laptop or computer after wearing glasses.
In these ways you can convince and encourage your friend.
Hope this helps:)