What this coin looks like (obverse, reverse, mint mark location, special features, etc.): One major variety of the 1840 Seated Liberty Half Dollar features the reverse of 1839 design which included a smaller eagle and small letters as depicted above. This coin was minted at the Philadelphia Mint.
The variety with the medium letters was actually struck using a die from the reverse of an older 1838 half dollar and was produced at the New Orleans - but did not have a mintmark on the coin! The difference between the 1840 Medium Letters vs Small Letters (Reverse of 1838 vs Reverse of 1839) is depicted below in the example comparison image of the coins:
Coin valuation chart: Typical coin prices, values and worth per grade or condition - in USD