They will lose quality, but as your TV is not HD that is not too much of an issue, however mosed paid for content has HDCP it means you will have problems with films etc that have it. I am not recommending from experience but this one claims to support HDCP. Just an example not a recommendation!
The TV requirement (from Apple site) is below so check you have the 720p and 50/60 Hz capability too.
- Compatible with high-definition TVs with HDMI and capable of 1080p or 720p at 60/50Hz,2 including popular models from these manufacturers: Hitachi, JVC, LG, Mitsubishi, NEC, Panasonic, Philips, Pioneer, Samsung, Sharp, Sony, Toshiba, Vizio, Westinghouse
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