Which of the following materials has maximum optical density?

Copy the figure and show the image formation with the help of rays.

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

In a plane mirror,the distance between the image and the mirror is the same as the distance between the object and the mirror.

$(a)$ $A$ concave mirror produces a three times enlarged real image of an object placed at $10\, cm$ in front of it. Calculate the focal length of the mirror.
$(b)$ Show the formation of the image with the help of a ray diagram when an object is placed $6\, cm$ away from the pole of a convex mirror.

Sudha finds out that the sharp image of the window pane of her science laboratory is formed at a distance of $15\, cm$ from the lens. She now tries to focus the building visible to her outside the window instead of the window pane without disturbing the lens. In which direction will she move the screen to obtain a sharp image of the building? What is the approximate focal length of this lens?