An object is placed on the principal axis of a convex lens of focal length $10\,cm$ as shown. $A$ plane mirror is placed on the other side of the lens at a distance of $20\,cm$. The final image produced by the plane mirror is $5\,cm$ behind the mirror. The distance of the object from the lens is $............cm$.

The camera lens has an aperture of $f$ and the exposure time is $(1/60) \, s$. What will be the new exposure time if the aperture becomes $1.4 \, f$?

$A$ ray of light enters from air into water. Which of the following figures shows the dispersion of light?

$A$ particle is oscillating on the $X-$ axis with an amplitude $2\, cm$ about the point $x_0 = 10\, cm$ with a frequency $\omega $. $A$ concave mirror of focal length $5\, cm$ is placed at the origin (see figure). Identify the correct statements.
$(A)$ The image executes periodic motion
$(B)$ The image executes non-periodic motion
$(C)$ The turning points of the image are asymmetric w.r.t the image of the point at $x = 10\, cm$
$(D)$ The distance between the turning points of the oscillation of the image is $\frac{100}{21}\, cm$

$A$ glass beaker has a solid,plano-convex base of refractive index $1.60$,as shown in the figure. The radius of curvature of the convex surface $(SPU)$ is $9 \ cm$,while the planar surface $(STU)$ acts as a mirror. This beaker is filled with a liquid of refractive index $n$ up to the level $QPR$. If the image of a point object $O$ at a height of $h$ ($OT$ in the figure) is formed onto itself,then which of the following option$(s)$ is (are) correct?
$(A)$ For $n=1.42, h=50 \ cm$
$(B)$ For $n=1.35, h=36 \ cm$
$(C)$ For $n=1.45, h=65 \ cm$
$(D)$ For $n=1.48, h=85 \ cm$

$A$ convex mirror and a concave mirror of radius $10\; cm$ each are placed $15\; cm$ apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in the convex mirror,the position of the final image is: