A refrigerator comprising: a cabinet forming a storage space; a main door to open and close the storage space and having an opening part; a sub door rotatably mounted on the main door to open and close the opening part; a panel assembly provided in the sub-door formed of a half mirror reflecting a part of light and transmitting a part of the light to be selectively transparent and allowing selectively viewing an inside of the opening part by a user; a lighting unit provided inside the refrigerator to emit light to illuminate the storage space, the light from the lighting unit passing through the panel assembly, wherein the refrigerator enables an inside of the refrigerator to be seen through while the lighting unit is turned on, and forms a mirror surface while the lighting unit is turned off; and a display unit provided inside the refrigerator to display an operation state of the refrigerator; a knock detection device provided in the sub door and detecting a user's knocking operation; wherein, if it is determined that the user's knocking operation is valid, the lighting unit is turned on according to the knock detection device detecting the user's knocking operation on a front surface of the sub door while the sub door is closed to make the panel assembly appear transparent and the display unit is turned on to allow determining the operation state from an outside of the refrigerator through the panel assembly; and wherein the panel assembly comprises: a front panel which forms an exterior of a front surface thereof, an insulation panel which is formed to be spaced apart from a rear surface of the front panel, and a spacer bar provided between the front panel and the insulation panel. a cabinet forming a storage space; a main door to open and close the storage space and having an opening part; a sub door rotatably mounted on the main door to open and close the opening part; a panel assembly provided in the sub-door formed of a half mirror reflecting a part of light and transmitting a part of the light to be selectively transparent and allowing selectively viewing an inside of the opening part by a user; a lighting unit provided inside the refrigerator to emit light to illuminate the storage space, the light from the lighting unit passing through the panel assembly, wherein the refrigerator enables an inside of the refrigerator to be seen through while the lighting unit is turned on, and forms a mirror surface while the lighting unit is turned off; and a display unit provided inside the refrigerator to display an operation state of the refrigerator; a knock detection device provided in the sub door and detecting a user's knocking operation; wherein, if it is determined that the user's knocking operation is valid, the lighting unit is turned on according to the knock detection device detecting the user's knocking operation on a front surface of the sub door while the sub door is closed to make the panel assembly appear transparent and the display unit is turned on to allow determining the operation state from an outside of the refrigerator through the panel assembly; and wherein the panel assembly comprises: a front panel which forms an exterior of a front surface thereof, an insulation panel which is formed to be spaced apart from a rear surface of the front panel, and a spacer bar provided between the front panel and the insulation panel. a front panel which forms an exterior of a front surface thereof, an insulation panel which is formed to be spaced apart from a rear surface of the front panel, and a spacer bar provided between the front panel and the insulation panel.