Theatre performer Ryan King, 21, used online messaging service Kik to contact the girl and struck up a number of conversations with her.
King, who plays the saxophone and piano, then sent the youngster a dozen pictures of his private parts over a two-week period last year.
He was caught as part of a UK-wide probe into online child abuse which revealed he had been sharing sick photographs with other users of a messaging service.
Police officers raided his home in Bothwell, Lanarkshire, in August last year and removed his laptop and iPad. They discovered 97 indecent images on the devices and found the messages sent to the young girl by King.
King, who studied music at Edinburgh College, had earlier admitted charges of distributing indecent images and causing an underage girl to look at naked images.
Yesterday at Hamilton Sheriff Court he was jailed for 18 months and ordered to be kept on licence for three and a half years on his release. He was also put on the Sex Offenders’ Register indefinitely.
Defence lawyer Ian Scott had asked for King to be spared jail and said he had been given a letter of support from his parish priest.
He said: “He acknowledges the behaviour is wrong but he has convinced himself that the people involved are not real.
“When he is dealing with people in real life he is a very accomplished person but there may be some removal from reality when he is operating a computer and there would require to be very strict use of electronic devices and he accepts that is inevitable.
“He comes from a very supportive family and some are away on holiday just now. He hopes to join them later if he is able to.
“They are all very concerned and the parish priest has written a letter to vouch for the family and for Mr King.
“He is a very hard working person in the church and devotes a lot of time to his studies.”
Procurator fiscal depute Jason Bell had earlier said: “The police received intelligence from the National Online Child Abuse Prevention department that a device was involved in accessing indecent images of children.
“Officers attended to carry out a search at the accused’s home and a pen drive within a laptop and an iPad were removed.
“An examination was carried out revealed indecent images of children and the accused admitted the images recovered were his.
“In the course of searching the items the police noticed there had been conversations via the Kik messenger application with a child of 11 years of age.”
Sheriff John Miller said: “You sent a number of images to an 11-year-old child and because of the gravity of your offending no other disposal is appropriate.
“You are at a high risk of sexual re-offending and a significant degree of harm was caused to those involved.
“You have not offended previously and come from a stable family background but that does not matter.
“Each child in the images you sent is a victim of sexual abuse and the 11-year-old child is also a victim.
“I am concerned that the general public is protected from significant harm when you are released.”
King’s not guilty pleas to further charges of taking and possessing indecent images and encouraging the girl to engage in sexual activity were accepted by prosecutors.