Four combinations of two thin lenses are given in$\mathrm{List}-\mathrm{I}$. The radius of curvature of all curved surface is $\mathrm{r}$ and the refractive index of all lenses is $1.5$. Match lens combinations in $\mathrm{List}-\mathrm{I}$ with their focal length in $\mathrm{List}-\mathrm{II}$ and select the correct answer using the code given below the lists.

 

Two identical glass rods $S_1$and $S_2$ (refractive index$=1.5$) have one convex end of radius of curvature $10 \mathrm{cm}$. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light $P$ is placed inside rod $S_1$ on its axis at a distance of $50 \mathrm{cm}$ from the curved face, the light rays emanating from it are found to be parallel to the axis inside ${\mathrm{S}}_2$. The distance $d$ is

A parallel beam of light is incident from the air at an angle $\alpha$ on the side $PQ$ of a right-angled triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face $PR$, when $\alpha$ has a minimum value of $45°$. The angle $\mathrm{\theta }$ of the prism is:

A plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30 \mathrm{cm}$ away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of $10 \mathrm{cm}$ away from the lens. Which of the following statement(s) is(are) true?

A transparent slab of thickness $d$ has a refractive index $n\left(z\right)$ that increases with $z$. Here, $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2\left(>n_1\right)$, as shown in the figure. A ray of light is incident with the angle ${\mathrm{\theta }}_{\mathrm{i}}$ from medium $1$ and emerges in medium $2$ with refraction angle ${\mathrm{\theta }}_{\mathrm{f}}$ with a lateral displacement $l$:

Which of the following statement(s) is (are) true?

A smaller object is placed $50 \mathrm{cm}$ to the left of a thin convex lens of focal length $30 \mathrm{cm}$. A convex spherical mirror of radius of curvature $100 \mathrm{cm}$ is placed to the right of the lens at a distance of $50 \mathrm{cm}$. The mirror is tilted such that the axis of the mirror is at an angle $\mathrm{\theta }=30°$ to the axis of the lens, as shown in the figure.

If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates $\left(\mathrm{in} \mathrm{cm}\right)$ of the point $\left(x, y\right)$ at which the image is formed are

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)