A periscope uses two plane mirrors inclined at 45^ ^ . If the tube...

The working of a periscope is based on the successive reflections of light from two plane mirrors placed parallel to each other and inclined at an angle of 45^{}^{\circ}.

The image formation by a plane mirror is governed by the laws of reflection, which state that the angle of incidence is equal to the angle of reflection. These laws are entirely independent of the refractive index of the surrounding medium.

When the tube of the periscope is filled with a completely transparent liquid of refractive index $1.5$, the light rays entering normally will undergo reflection at the same angles (45^{}^{\circ}$) as they would in air. Since the liquid is completely transparent, there is no absorption of light, meaning the brightness of the image will not be altered by a factor of 1.5$.

Because the geometry of reflection remains unaffected by the change in the medium, the position, size, and nature of the image will remain unchanged.