You have the right adapter, but it's only 6" long. You're going to need an extension cord for the headphones unless the TV is right next to your bed. I've purchased a significant number of various cables through amazon and I have yet to be disappointed. I've actually been pleasantly surprised by the quality, except for the last adapter I bought. It is kind of poorly constructed, but it works fine. I've bought three double male end RCA cable pairs, 2- 50 ft and one 25 ft, and an HDMI cable, and two of the 3.5mm stereo adapters. (I broke one, but that was my fault) I've even put to use a switch I bought a long while ago so I can switch from my sound card output between the stereo & the headphones. I haven't had to return any of them for any types of defects. I've got my turntable going to the computer so I can record my Vinyl to hard disk. I also have the TV going to the stereo and an HDMI cable going from the computer to the TV. It's a cable maze for the novice, but they all work as I wanted them to work. The last TV I had in the bedroom, I disconnected the speaker and ran it to an RCA jack and ran it to an old pair of computer speakers. I need to do the same to the current tv as it has no jacks.
Ohh, and I've tried those "wireless headphones" and they are JUNK. The sound quality is poor and they are prone to interference. Besides, I can't sleep with stuff in my ears.