The distance between a convex lens and a plane mirror is $10 \, cm$. The parallel rays incident on the convex lens after reflection from the mirror form an image at the optical centre of the lens. The focal length of the lens will be.....$cm$.

An equiconvex lens of glass of focal length $0.1 \text{ m}$ is cut along a plane perpendicular to the principal axis into two equal parts. The ratio of the focal lengths of the new lenses formed is

$A$ luminous object is placed at a distance of $30 \,cm$ from a convex lens of focal length $20 \,cm$. On the other side of the lens,at what distance from the lens should a convex mirror of radius of curvature $10 \,cm$ be placed in order to have an upright image of the object coincident with it (in $,cm$)?

An equiconvex lens is cut into two parts along its $(i) \ XOX'$ axis and $(ii) \ YOY'$ axis as shown in the figure. Let $f, f', f''$ be the focal lengths of the original lens,each half in the first case,and each half in the second case,respectively. Which of the following statements is correct?

If a lens is cut into two pieces perpendicular to the principal axis and only one part is used,the intensity of the image

An object is placed at a distance of $12 \,{cm}$ from a convex lens. $A$ convex mirror of focal length $15 \,{cm}$ is placed on the other side of the lens at $8 \,{cm}$ as shown in the figure. The image of the object coincides with the object. When the convex mirror is removed,a real and inverted image is formed at a position. The distance of this image from the object will be ..... $(cm)$.