The upper and lower portions in common type of bi-focal lenses are respectively:

The correct answer is option 'A' - Concave and convex.

Explanation:

Bi-focal lenses are used to correct vision problems that occur due to presbyopia, which is the natural aging process of the eye that causes difficulty in focusing on near objects. These lenses consist of two distinct optical powers, usually divided into two sections - the upper and lower portions.

Upper Portion:
The upper portion of a common type of bi-focal lens is concave. Concave lenses are thinner at the center and thicker at the edges. They are used to correct nearsightedness (myopia) by diverging the light rays to focus them properly on the retina.

Nearsightedness is a condition where distant objects appear blurry, and a concave lens helps to correct this by spreading out the light rays before they enter the eye, allowing them to focus properly on the retina.

Lower Portion:
The lower portion of a common type of bi-focal lens is convex. Convex lenses are thicker at the center and thinner at the edges. They are used to correct farsightedness (hyperopia) by converging the light rays to focus them properly on the retina.

Farsightedness is a condition where near objects appear blurry, and a convex lens helps to correct this by bending the light rays towards each other before they enter the eye, allowing them to focus properly on the retina.

The combination of concave and convex lenses in a bi-focal lens allows individuals to have clear vision for both near and distant objects. The upper portion corrects nearsightedness, while the lower portion corrects farsightedness.

It is important to note that bi-focal lenses can also have variations, such as progressive lenses, which provide a seamless transition between different optical powers, eliminating the visible line between the upper and lower portions.

In summary, the upper portion of a common type of bi-focal lens is concave, while the lower portion is convex.