What is the distance between the principal focus and the center of curvature of a spherical mirror?

$(a)$ $A$ converging lens forms a real and inverted image of an object at a distance of $100 \, cm$ from it. Where should an object be placed in front of the lens so that the size of the image is twice the size of the object? Also, calculate the power of the lens.
$(b)$ State the laws of refraction.

Where is the object placed in a compound microscope?

The magnification of a real image formed by a concave mirror is always ...

$A$ child is standing in front of a magic mirror. She finds the image of her head bigger, the middle portion of her body of the same size, and that of the legs smaller. What is the order of combinations for the magic mirror from the top?

$(a)$ Define principal focus of a spherical mirror.
$(b)$ For what position of the object does a concave mirror form a real,inverted and diminished image of the object? Draw the ray diagram.
$(c)$ An object $4 \,cm$ high is placed at a distance of $6 \,cm$ in front of a concave mirror of focal length $12 \,cm$. Find the position of the image formed.