Well, double vision has a medically name, which is diplopia. Opening eyes and seeing a single, clear image must depend on the orchestration of multiple areas of the vision system. Double vision is the simultaneous perception of two images of a single object that may be displaced horizontally, vertically, or diagonally in relation to each other. Sleep deprivation means people are lack of sleeping, which can be clarifies as chronic or acute. A chronic sleep-restricted state can cause fatigue, daytime sleepiness, clumsiness and weight loss or weight gain that affects the brain and cognitive function deeply. Sleep deprivation is easy to cause oxygen and blood shortage in brain so that the nerves cannot work normally. If we cannot receive the right order which given by nerves, then double vision is easy to occur. However, double vision may be also due to migraine, cancer, trauma and so on. So the best thing to do is to call for a doctor to get the real reason for your double vision.
As to your question, I can see your eyes have got some problems, which gave rise to some discomfort and troubles. Anyway, sleep deprivation would lead to a lot of problems to every part of your body,including double vision or blurred vision, so you have to take it seriously and take actions against it by getting regular rest and consult a doctor. Also try to get some exercise and make your life in order. Some vitamin pills and nutrition would also help you with your problem.
Yes, it is normal that your sleep deprivation causes double vision. It is not a sign of myopia. Your eyes nerves will be affected and get tired. You need to use the eye drops to moisture the eyes and release the symptom of double vision. You could also use the warm compress to make your eyes feel comfortable. You should not stay up late at night which will be really bad for the health of eyes.