$A$ biconvex lens $(R_1 = R_2 = 30 \ cm)$ has a focal length equal to the focal length of a concave mirror. What is the radius of curvature of the concave mirror (in $cm$)? (Refractive index of the material of the lens $\mu = 1.6$)

$A$ small object is placed $50 \ cm$ to the left of a thin convex lens of focal length $30 \ cm$. $A$ convex spherical mirror of radius of curvature $100 \ cm$ is placed to the right of the lens at a distance of $50 \ cm$. The mirror is tilted such that the axis of the mirror is at an angle $\theta=30^{\circ}$ to the axis of the lens,as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens,the coordinates (in $cm$) of the point $(x, y)$ at which the image is formed are

The $45^{\circ}-45^{\circ}-90^{\circ}$ prism of height $10 \,cm$ (see image) has a refractive index $\mu = 2$,with a silvered hypotenuse surface. $A$ convex lens of focal length $10 \,cm$ is placed $15 \,cm$ in front of a wall. The system produces a sharp image of point $P$ on the wall. The value of $h$ (in $cm$) is closest to:

$A$ wire is bent in the shape of a right-angled triangle and is placed in front of a concave mirror of focal length $f$,as shown in the figure. Which of the figures shown in the four options qualitatively represent$(s)$ the shape of the image of the bent wire? (These figures are not to scale.)

$A$ 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

Assertion: By roughening the surface of a glass sheet,its transparency can be reduced.
Reason: Glass sheet with a rough surface absorbs more light.