$A$ small source of light is to be suspended directly above the centre of a circular table of radius $R$. What should be the height of the light source above the table so that the intensity of light is maximum at the edges of the table compared to any other height of the source?

$A$ plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30 \ cm$ 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 curved surface of the lens,another faint image is observed at a distance of $10 \ cm$ away from the lens. Which of the following statement$(s)$ is(are) true?
$(A)$ The refractive index of the lens is $2.5$
$(B)$ The radius of curvature of the convex surface is $45 \ cm$
$(C)$ The faint image is erect and real
$(D)$ The focal length of the lens is $20 \ cm$

If the polarising angle of a piece of glass for green light is $54.74^o$,then the angle of minimum deviation for an equilateral prism made of the same glass is......$^o$ (Given $\tan 54.74^o = 1.414$)

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l > 0$ from one of the corners as shown in the figure. $A$ ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.
Which of the following statement(s) is(are) correct?
$(A)$ The ray of light will come out for $\theta=30^{\circ}$, for $0 < l < L$.
$(B)$ There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
$(C)$ The ray of light will $NEVER$ come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
$(D)$ The ray of light will come out for $\theta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.

$A$ luminous object is placed $20 \, cm$ from the surface of a convex mirror and a plane mirror is adjusted in such a way that the virtual images formed by the two mirrors coincide. If the focal length of the convex mirror is $5 \, cm$,then the distance between the plane mirror and the object will be......$cm$.

$A$ small fish,$0.4\,m$ below the surface of a lake,is viewed through a simple converging lens of focal length $3\,m$. The lens is kept at $0.2\,m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at $\left( \mu_{water} = \frac{4}{3} \right)$