Which of the following is $NOT$ involved in the formation of a secondary rainbow?

$A$ cubic block of glass with refractive index $n_1$ is in contact with the surface of water with refractive index $n_2$. $A$ ray of light is incident on the vertical face of the block (see figure). After refraction,total internal reflection at the base,and refraction at the opposite vertical face,the ray emerges at an angle $\theta$. The value of $\theta$ is given by:

Total flux produced by a source of $1 \ cd$ is

An optical arrangement consists of two concave mirrors $M_1$ and $M_2$,and a convex lens $L$ with a common principal axis,as shown in the figure. The focal length of $L$ is $10 \text{ cm}$. The radii of curvature of $M_1$ and $M_2$ are $20 \text{ cm}$ and $24 \text{ cm}$,respectively. The distance between $L$ and $M_2$ is $20 \text{ cm}$. $A$ point object $S$ is placed at the mid-point between $L$ and $M_2$ on the axis. When the distance between $L$ and $M_1$ is $n/7 \text{ cm}$,one of the images coincides with $S$. The value of $n$ is. . . .

An object is placed in front of a convex mirror at a distance of $50 \ cm$. $A$ plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30 \ cm$,it is found that there is no gap between the images formed by the two mirrors. The radius of the convex mirror is .......$cm$.

$A$ diverging lens of focal length $10 \, cm$ is placed $10 \, cm$ in front of a plane mirror as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance