An object is placed $20 \, cm$ in front of a convex mirror. $A$ plane mirror is also placed such that the virtual images formed by both mirrors coincide. If the plane mirror is placed $15 \, cm$ from the object,find the focal length of the convex mirror in $cm$.

Correct exposure for a photographic print is $10 \, s$ at a distance of $1 \, m$ from a point source of $20 \, cd$. For an equal fogging of the print placed at a distance of $2 \, m$ from a $16 \, cd$ source,the necessary time for exposure is.......$s$.

When a pin is moved along the principal axis of a small concave mirror,the image position coincides with the object at a point $0.5\, m$ from the mirror. If the mirror is placed at a depth of $0.2\, m$ in a transparent liquid,the same phenomenon occurs when the pin is placed $0.4\, m$ from the mirror. The refractive index of the liquid is

The exposure time of a camera lens at the $f/2.8$ setting is $1/200$ second. The correct time of exposure at $f/5.6$ is......$sec$

An opaque card is held over the lower half of a converging lens as shown in the figure. Which picture best shows the image that appears on the screen?

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 ..... $cm$.