Talk about how endoscopes use optical fibres.
Then talk about how you want maximum transmission of light along the fibres and minimum loss.
Then talk about how total internal reflection to keep the light within the fibre. A diagram is useful here.
In answering this question what you need to do is explain (relate cause and effect) how endoscopes work in realtion to total internal reflection.
Sample answer: Endoscopes consist of two distinct layers, an inner core and an outer layer of cladding. The higher refractive index core will reflect light waves off it's boundaries when the angle of incidence exceeds the critical angle for that particular material (core). The cladding helps to maintain all of the light within the endoscope and a black sheath over the endoscope will mean light from the external environment will not enter. As the light enters at an angle greater than the critical angle it will be totally internally reflected and bounce along the walls of the tubes. In this way, light is able to be bent around corners.