An equiconvex lens of focal length $f$ and power $P$ is cut into two halves in thickness. What are the focal length and power of each half?

Sunglasses (goggles) have curved surfaces, yet their power is zero, why?

A lens of focal length $f$ forms the image of a luminous object on a screen $m$ times large. Show that the distance of the screen from the lens is $f(1+m)$.

Use the lens equation to explain that an object placed within the focus of a convex lens produces a virtual, enlarged image.

Use the lens equation to explain that a concave lens produces a virtual and diminished image, independent of the location of the object.

State how focal length of a glass lens (refractive index $1.5$) changes when it is completely immersed in Water (refractive index $1.33$).

State how focal length of a glass lens (refractive index $1.5$) changes when it is completely immersed in A liquid (refractive index $1.65$).