An object is placed at a distance of $50 \, cm$ in front of a convex mirror. $A$ plane mirror is inserted covering half of the convex mirror. If the distance between the object and the plane mirror is $30 \, cm$,it is observed that there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror is ..... $cm$.

$A$ camera objective has an aperture diameter $d.$ If the aperture is reduced to diameter $d/2,$ the exposure time under identical conditions of light should be made

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 $..........$

$A$ $60 \text{ W}$ bulb is hung over the center of a table of size $4 \text{ m} \times 4 \text{ m}$ at a height of $3 \text{ m}$. The ratio of the intensities of illumination at a point on the center of the edge $(A)$ and at the corner of the table $(B)$ is:

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 $\tan 54.74^o = 1.414$)

Ray optics is valid when characteristic dimensions are: