$A$ lamp is hanging at a height of $4\,m$ above a table. The lamp is lowered by $1\,m$. The percentage increase in illuminance will be.....$\%$

$A$ small object is placed $50 \ cm$ to the left of a thin convex lens of focal length $30 \ cm$. $A$ convex spherical mirror of radius of curvature $100 \ cm$ is placed to the right of the lens at a distance of $50 \ cm$. The mirror is tilted such that the axis of the mirror is at an angle $\theta=30^{\circ}$ 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 (in $cm$) of the point $(x, y)$ at which the image is formed are

For a concave mirror,if a real image is formed,the graph between $\frac{1}{u}$ and $\frac{1}{v}$ is of the form:

$A$ photograph of the moon was taken with a telescope. Later on, it was found that a housefly was sitting on the objective lens of the telescope. In the photograph:

$A$ lamp is hanging $1 \, m$ above the center of a circular table of diameter $1 \, m$. The ratio of illuminances at the center and the edge is:

An optical component and an object $S$ placed along its optic axis are given in Column $I$. The distance between the object and the component can be varied. The properties of images are given in Column $II$. Match all the properties of images from Column $II$ with the appropriate components given in Column $I$.

Column $I$	Column $II$
$A$. Concave Mirror	$(p)$ Real image
$B$. Convex Mirror	$(q)$ Virtual image
$C$. Convex Lens	$(r)$ Magnified image
$D$. Concave Lens	$(s)$ Image at infinity