How do I send an image to the output in JSP

I want to open my servlet which basically checks my permissions and if allowed, shows me a picture like it would be a real jpeg. My code so far:

File file = new File("C:/test.jpeg");
FileInputStream fis = new FileInputStream(file);
byte imageBytes[] = new byte[(int) file.length()];
    
response.setContentType("image/jpeg");
response.setContentLength(imageBytes.length);
response.getOutputStream().write(imageBytes);
response.getOutputStream().flush();

But somehow the image it tries to show me in the browser is corrupted. I already checked that the file exists, as the image.length is not zero. What did I do wrong?