$Lux$ is equal to:

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 $1.5 \times 10^{11} \, m$.

If $\hat{n}_1$ is the unit vector along the incident ray,$\hat{n}_2$ is the unit vector along the normal,and $\hat{n}_3$ is the unit vector along the reflected ray,then which of the following must be true?

$A$ 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......$cm$.

$A$ student measures the focal length of a convex lens by obtaining an image of an object pin at a distance '$v$' from the lens,where the object pin is at a distance '$u$' from the lens. What will the graph between '$u$' and '$v$' look like?

$A$ 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.....$\%$