An object is placed $50\, cm$ from a lens that produces a virtual image at a distance of $10\, cm$ in front of the lens. Calculate the focal length of the lens. (in $, cm$)

What is the $SI$ unit of the power of a lens?

With the help of a ray diagram,show that the angle of incidence is equal to the angle of reflection when a ray is incident on a concave mirror.

An object is placed $15\, cm$ from a convex mirror of radius of curvature $60\, cm$. Find the position of the image and its magnification.

For what position of the object does a concave mirror form a real and diminished image?

$(a)$ $A$ 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.