Show her the machine

"It's a tanning booth."

"I promise it's much more than that. If you look closely at the bulbs you'll see the difference straight away."

She seems hesitant, but complies. Now that she's inside the machine you have a decision to make - Do you shut the door and activate the machine, this would make her more compliant to your proposal but could raise some suspision; or do you let this play out and hope her that inspection of the machine has convinced her.