The figure shows a triangular prism of glass in the air, an incident ray enters the glass perpendicular to one face and is totally reflected at the glass-air interface as indicated. If ${\mathrm{\theta }}_1$ is $45°$ and $n$ is the refractive index of glass, then

A medium with refractive index $n\left(\mathrm{\omega }\right)$, where $\mathrm{\omega }$ is the angular frequency, is said to possess anomalous dispersion when

Two thin convex lenses $L_1$ and $L_2$ with focal lengths $1 \mathrm{cm}$ and $2 \mathrm{cm}$ respectively are separated by a distance of $4 \mathrm{cm}$ along their axis. An object is placed at a distance of $1.5 \mathrm{cm}$ before the first lens. The ratio of the final image size to the object size is