Concept:
An endoscope uses optical fibres to transmit light and images from inside the body to the observer.
Step 1: Optical fibres work on the principle of total internal reflection.
Step 2: In total internal reflection, light travelling from a denser medium to a rarer medium is completely reflected back into the denser medium if the angle of incidence is greater than the critical angle.
Step 3: In an optical fibre, light undergoes repeated total internal reflections inside the fibre.
Step 4: This allows light to travel through curved paths without escaping.
Step 5: Since endoscopes use optical fibres, their working principle is total internal reflection.
\[
\boxed{\text{Total internal reflection}}
\]