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Copyright law has no provision that permits you to acquire rights to a photo simply because you're the subject of the photo. The exception is a selfie in which the photographer and the subject are the same (provided you're not a monkey). The copyright can still be acquired by a transfer (assignment) but you'll need to track down the copyright owner -- possibly the newspaper under work for hire rules, or the photographer's estate. There are, however, three other legal bases for prohibiting publication of the photo.
Defamation. Defamation occurs if publishing the photo creates a false impression and injures your reputation. Unless the photo materially ridicules, humiliates, or subjects you to contempt, you'll have a hard time claiming defamation.
Invasion of privacy. Your privacy can be invaded if the photo falsely portrays you in a highly offensive manner; if the photo discloses private or embarrassing facts about you without relation to a legitimate public concern; or if the photographer intruded on you to take the photo in a situation where you had a reasonable expectation of privacy. However, it is not an invasion of privacy to photograph someone in a public place or at any event where the public is invited. Such photos can be used freely for informational purposes, provided that the use does not defame or hold you up to a false light. Because the photo was published 35 years ago and you have not objected until now, we think you may have a hard time claiming your privacy is invaded.
Right of publicity. The right of publicity prohibits using your image to imply that you endorse a product. The use of the photo for news, information, or public interest purposes is not a violation of the right of publicity. If the photo is used to sell products (for example, a mattress ad) you could have a claim for violation of your right of publicity.