A beam of polychromatic light passes through a thin prism of prism angle $6^{\circ}$. The refractive index of the material of the prism varies with wavelength $(\lambda)$ as $n(\lambda) = \alpha \lambda + \frac{\beta}{\lambda^2}$, where $\alpha = 3\ \mu m^{-1}$ and $\beta = 0.096\ \mu m^2$. If $\lambda_{min}$ is the wavelength at which the angle of minimum deviation $D_m$ is smallest, then the correct value of $D_m$ at $\lambda_{min}$ is :
A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index nL. The correct plot showing the variation of the power, in the units of diopter (D), as a function of nL is :
A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_0$. The ray partially refracts into the sphere with angle of refraction $\phi_0$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
| List-I | List-II |
|---|---|
| (P) If $n = 2$ and $\alpha = 180^\circ$, then all the possible values of $\theta_0$ will be | (1) $30^\circ$ and $0^\circ$ |
| (Q) If $n = \sqrt{3}$ and $\alpha = 180^\circ$, then all the possible values of $\theta_0$ will be | (2) $60^\circ$ and $0^\circ$ |
| (R) If $n = \sqrt{3}$ and $\alpha = 180^\circ$, then all the possible values of $\phi_0$ will be | (3) $45^\circ$ and $0^\circ$ |
| (S) If $n = \sqrt{2}$ and $\theta_0 = 45^\circ$, then all the possible values of $\alpha$ will be | (4) $150^\circ$ |
| (5) $0^\circ$ |
List I contains four combinations of two lenses (1 and 2) whose focal lengths (in $\mathrm{cm}$ ) are indicated in the figures. In all cases, the object is placed $20 \mathrm{~cm}$ from the first lens on the left, and the distance between the two lenses is $5 \mathrm{~cm}$. List II contains the positions of the final images.
| List-I | List-II |
|---|---|
(I)  |
(P) Final image is formed at $7.5 \mathrm{~cm}$ on the right side of lens 2 . |
(II)  |
(Q) Final image is formed at $60.0 \mathrm{~cm}$ on the right side of lens 2 . |
(III)  |
(R) Final image is formed at $30.0 \mathrm{~cm}$ on the left side of lens $2 .$ |
(IV)  |
(S) Final image is formed at $6.0 \mathrm{~cm}$ on the right side of lens 2 . |
| (T) Final image is formed at $30.0 \mathrm{~cm}$ on the right side of lens 2 . |
Which one of the following options is correct?
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