Question #43228

A compound microscope is constructed using an objective lens of focal length $f_o = 2.0 \text{ cm}$ and an eyepiece of focal length $f_e = 6.0 \text{ cm}$. An object is placed at a distance of $2.5 \text{ cm}$ in front of the objective. To make the instrument compact, a right-angled glass prism of refractive index $n = 1.5$ is inserted between the lenses to fold the light path via Total Internal Reflection. The physical length of the light path inside the glass prism is $t = 6.0 \text{ cm}$. If the final virtual image is formed at a distance of $D = 30.0 \text{ cm}$ from the eyepiece, calculate the total physical path length $L$ of the central light ray between the objective and the eyepiece. (Assume paraxial rays and that the unfolded prism acts equivalently to a glass slab of thickness $t$).