The radius of curvature of a concave mirror is $40 \ cm$ and the size of the image is twice that of the object. The object distance is $... \ cm$.

$A$ concave mirror of focal length $15\, cm$ forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be........$cm$

The cross-section of a reflecting surface is represented by the equation $x^{2}+y^{2}=R^{2}$ as shown in the figure. $A$ ray travelling in the positive $x$ direction is directed toward the positive $y$ direction after reflection from the surface at point $M$. The coordinate of the point $M$ on the reflecting surface is

$A$ convex lens (of focal length $20\, cm$) and a concave mirror,having their principal axes along the same lines,are kept $80\, cm$ apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of $30\, cm$ to the left of the convex lens,its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror,by itself,would produce a virtual image would be.....$cm$.

Suppose that the lower half of the concave mirror's reflecting surface in the figure is covered with an opaque (non-reflective) material. What effect will this have on the image of an object placed in front of the mirror?

$A$ small candle,$2.5\; cm$ in size,is placed at $27\; cm$ in front of a concave mirror of radius of curvature $36\; cm$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror,how would the screen have to be moved?