$A$ point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance $E$ at this portion varies with its distance $r$ from the source as:

$A$ hemispherical glass body of radius $10\, cm$ and refractive index $1.5$ is silvered on its curved surface. $A$ small air bubble is $6\, cm$ below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

In an experiment for estimating the value of focal length of a converging mirror,the image of an object placed at $40\,cm$ from the pole of the mirror is formed at a distance of $120\,cm$ from the pole of the mirror. These distances are measured with a modified scale in which there are $20$ small divisions in $1\,cm$. The value of error in the measurement of the focal length of the mirror is $1/K\,cm$. The value of $K$ is $..........$

An object is placed $60 \ cm$ in front of a convex mirror of focal length $30 \ cm$. $A$ plane mirror is now placed facing the object in between the object and the convex mirror such that it covers the lower half of the convex mirror. What should be the distance of the plane mirror from the object so that there will be no parallax between the images formed by the two mirrors (in $cm$)?

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 $\tan 54.74^o = 1.414$)

$A$ horizontal parallel beam of light passes through a vertical convex lens of focal length $20 \,cm$ and is then reflected by a tilted plane mirror,so that it converges to a point $I$. The distance $P I$ is $10 \,cm$. $M$ is a point at which the axis of the lens intersects the mirror. The distance $P M$ is $10 \,cm$. The angle which the mirror makes with the horizontal is (in $^{\circ}$)