Image formation by refraction from plane and curved surface

A point object lies 30 cm above water on the axis of a convex mirror of focal length 40 cm lying 20 cm below water surface. Consider two images. (i) Image formed by the partial reflection from water surface. (ii) Image formed by refraction from water surface followed by reflection from mirror and again refraction out of the water surface. find the distance between these two images.

An extended object of size 2cm is placed at a distance of 10cm in air (n = 1) form pole, on the other side of refracting surface has refractive index n = 2 . Find the positon, nature and size of image formed after single refraction through the curved surface.

An extended object of size 2 cm is placed at a distance of 10 cm in air (n = 1) from pole, on the principal axis of a spherical curved surface. The medium on the other side of refracting surface has refractive index n = 2. Find the position, nature and size of image formed after single refraction through the curved surface.

Plane surface of a thin planoconvex lens reflects 50% of light, while the curved surface is completely transparent, if final image of O after refraction through lens coinsides with the image formed due to partial reflection from plane surface. if distance (in m) between O and lens is x then find x//4

Are the laws of refraction applicable to the refraction taking place at curved surfaces?

Refraction at curved surface and Lens

Image Formation From Plane Mirror

At what distance eye E will observe the fourth image (after four refractions from plane surfaces) of object O from itself.

Image formation by combination OF two plane mirrors|| reflection in vector form

The image for the converging beam after refraction through the curved surface is formed at