A person can focus objects when they lie beyond 75 cm from his eyes. The focal length of the lens required to reduce his least distance of distinct vision t...

A person can focus objects when they lie beyond 75 cm from his eyes. The focal length of the lens required to reduce his least distance of distinct vision to 25 cm is?

Answer Details

The question is asking for the focal length of a lens that will enable a person to focus on objects at a closer distance than they currently can. The given information is that the person's least distance of distinct vision (or near point) is 75 cm, which means that they can focus on objects only if they are beyond 75 cm from their eyes. To be able to focus on objects that are closer, the person needs a lens with a focal length such that the image of an object at a distance of 25 cm from the eye is formed at the person's least distance of distinct vision, which is 75 cm. This means that the lens should form a virtual image of the object at 25 cm on the other side of the lens, which then acts as the object for the eye. Using the lens formula, 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance (25 cm), and u is the object distance (the distance at which the virtual image is formed), we can find the value of u. 1/f = 1/v - 1/u 1/f = 1/25 - 1/u 1/f = (u - 25)/25u 25u/f = u - 25 25u = uf - 25f u = (25f)/(f + 25) Now, we know that the person's least distance of distinct vision is 75 cm, so the object distance u should be 75 cm. Substituting this in the above equation, we get: 75 = (25f)/(f + 25) Multiplying both sides by (f + 25), we get: 75f + 1875 = 25f Simplifying and solving for f, we get: f = 37.5 cm Therefore, the focal length of the lens required to reduce the person's least distance of distinct vision to 25 cm is 37.5 cm.