Show that for an object lying under a parallel glass slab, the apparent displacement of its image in the observer's direction does not depend on the position of the object.

An object is placed in front of a convex mirror on the principal axis. With the help of a ray diagram show the position of the image.

An object is placed just at the middle point between concave mirror of radius of curvature 40 cm and a convex mirror of radius of curvature 30 cm facing each other. The mirrors are situated 50 cm apart from each other. The mirrors are situated 50 cm apart from each other. Considering the first reflection occurs in the concave mirror, determine the position and nature of the image formed by this mirror. Next find the position and nature of the image formed by the convex mirror considering the first image for concave mirror as its object.

A glass is filled with water up to 12.5 cm. The apparent depth of an object lying at the bottom of the glass is measured by a microscope to be 9.4 cm. Calculate the refractive index of water. If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope has to be moved to focus the object again?