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• n  the quality of being intent and concentrated
  the intentness of his gaze

• In heroic days, now several centuries past, when two opposing armies debouched upon a field of battle, each advanced a herald to warn the other of its aims, the intentness of .
• As the ball whipped toward the plate, the batter's cool blue eyes examined it with icy intentness.
• From boyhood Frank Murphy had had a kind of desperate intentness.

• engrossment

News & Articles

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• David Denby: “Jack Ryan: Shadow Recruit,” “Gloria” reviews.
  Chris Pine has startlingly bright blue eyes, thick, dark eyebrows, and a way of seeming to look for something special even when he’s just staring into space—a gift of intentness that works well for him in “Jack Ryan: Shadow Recruit,” where he plays the . . . (Subscription required.)
  Jan. 13, 2014 - The New Yorker

Quotes

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• Theodore Roosevelt in New York Times
  More than a century ago, Teddy Roosevelt noted in that speech the particular limitation of "the man who in this life consistently refuses to see aught that is lofty, and fixes his eyes with solemn intentness only on that which is vile and debasing."