The radius of curvature of a spherical mirror is half of the focal length.

$(a)$ Calculate the distance at which an object should be placed in front of a convex lens of focal length $10\, cm$ to obtain a virtual image of double its size.
$(b)$ In the above given case,find the magnification,if the image formed is real. Express it in terms of the relation between $v$ and $u$.

Which of the following statements is true for light waves?

How will you identify a concave lens by touching it?

With the help of a ray diagram,show the formation of an image by a convex lens when the object is placed between $F$ and $2F$. Write two characteristics of the image so formed.

Which type of reflection will be represented by light reflected from a book?