The phrase "desk light" is correct and commonly used in written English.
It refers to a small, portable light that is specifically designed for use on a desk or workspace. Example: I couldn't see well enough to finish my work, so I turned on my desk light and continued typing away.
The Solar Muscle, a solar lamp made by Flexiway, can be used as a desk light.
My camera quality wasn't that good, and I used to make my films in the evenings using a desk light.
Sit in the chair, and the desk light goes on; get up, and the overhead lights brighten.
Bleary-eyed, you stumble away from your desk, switch off the desk light and pick up your phone to set an alarm for the morning.
The third, No. 1210, was perfect -- except that the desk light was unplugged, and neither of us could find the outlet.
In his supersleek offices there's little to dispute the claim: 29 pale wood desks; 29 Artemide desk lights; 29 flat-screen Macs.
The confederation's newsletter reprinted the opening two-page spread in a recent issue of Paris-Match that shows Mr. Sarkozy at his desk, lighting a cigar.
For the New York guest rooms, she and Mr. Calderwood have repurposed plumbing pipe as robe hooks and hang bars (which they are also introducing as a product line, at romanandwilliams.com) and installed inexpensive industrial swing-arm lamps as desk lighting.
On March 1 , 1985 Herbert Kretzmer, a droll, rangy South African lyricist, came home from his day job as a TV critic for the Daily Mail, climbed the steps to his London flat, put a Teddy bear — a Christmas gift from Terence Stamp — on his desk, lit a candle, and tacked a motto onto the wall in front of him.
Dropping her canvas bag on the floor, she sat crosslegged on top of her wooden desk, lit a cigarillo, took a few puffs from it, and then either crushed it out on her shoe and returned it to the pack or just crushed it out in the pack itself.
