Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of $10000 \, cd$ at a distance of $0.3 \, m$. The distance between the sun and the earth is $1.5 \times 10^{11} \, m$.

$A$ 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

$A$ 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?

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 parallax between the images formed by the two mirrors. The magnification of the convex mirror will be......

An optical bench has a $1.5 m$ long scale having four equal divisions in each $cm$. While measuring the focal length of a convex lens,the lens is kept at the $75 cm$ mark of the scale and the object pin is kept at the $45 cm$ mark. The image of the object pin on the other side of the lens overlaps with the image pin that is kept at the $135 cm$ mark. In this experiment,the percentage error in the measurement of the focal length of the lens is. . . . .