Need assistance with program for POV Project
Your third delay is the issue. It means you have up to 10 ms before you notice the need to turn on the light. Try this:

const byte pin = 13; 
volatile bool detected; 

void setup() { 
  pinMode(pin, OUTPUT); 
  attachInterrupt(1, blink, RISING); 
} 

void loop() { 
  if (detected)
    {
    delay(10);
    digitalWrite(pin, LOW);
    detected = false;
    }

} 

void blink() { 
  digitalWrite(pin, HIGH);
  detected = true; 
}


Now that immediately turns on the LED, so it will always happen at the same time. Then in the main loop you notice it is on, wait 10 ms, and then turn it off.