Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $n_1$ surrounded by a medium of lower refractive index $n_2$. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $n_1$ and $n_2$ as shown in the figure. All rays with the angle of incidence $i$ less than a particular value $i_m$ are confined in the medium of refractive index $n_1$ . The numerical aperture (NA) of the structure is defined as $\sin i_m$.

If two structures of same cross-sectional area, but different numerical apertures $\mathrm{N}{\mathrm{A}}_1$ and $\mathrm{N}{\mathrm{A}}_2$ $\left(\mathrm{N}{\mathrm{A}}_2<\mathrm{N}{\mathrm{A}}_1\right)$ are joined longitudinally, the numerical aperture of the combined structure is

An extended object is placed at point $O$, $10 \mathrm{cm}$ in front of a convex lens $L_1$ and a concave lens $L_2$ is placed $10 \mathrm{cm}$ behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are $20 \mathrm{cm}$. The refractive index of both the lenses is $1.5$. The total magnification of this lens system is:

A wide slab consisting of two media of refractive indices $n_1$ and $n_2$ is placed in air as shown in the figure. A ray of light is incident from medium $n_1$ to $n_2$ at an angle $\theta$, where $\sin \theta$ is slightly larger than $\frac{1}{n_1}$. Take refractive index of air as $1$. Which of the following statement(s) is (are) correct?

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)