A person suffering from far – sightedness wears a spectacle having a convex lens of focal length 50 cm. What is the distance of the near point of his eye?

The condition of far-sightedness, also known as hypermetropia, means that the person can see distant objects clearly but has difficulty focusing on near objects. This is corrected by using a convex lens.

The formula used to calculate the distance of the near point for a hypermetropic eye is:

1/v - 1/u = 1/f

Where: v = image distance (distance of the near point) u = object distance (distance from the lens to the object) f = focal length of the lens

In this case, the person is using a spectacle with a convex lens of focal length 50 cm. The standard near point for a normal eye is 25 cm. So, we can set u = -25 cm (the negative sign indicates that the object is on the same side of the lens as the light being bent).

Substituting these values into the formula gives:

1/v - 1/(-25) = 1/50

Solving this equation for v will give the distance of the near point for the person's eye.