Question

Hemulens has grown old and farsighted. In order to read his notes, Hemulens needs reading glasses with refractive power of +2 diopters. Fully relaxed, his eye’s focal length is 2.6 cm, and the distance from the lens of the eye to the retina is 2.5 cm. While searching for rare flora, Hemulens needs to both see the flora (through his magnifying glass) and read his notes perfectly. Is this possible? You may assume that the glasses are extremely close to the cornea and that the magnifying glass is at its optimal position (object at the front focal point).

Answer 1

The fully relaxed focal length of Hemulens' eye is 2.6 cm.

The retina, that is the screen of the eye is 2.5 cm away from the lens with focal length 2.6.

Now, the image of the object must fall on the retina to get a clear vision. so, to adjust the focal length, a reading glass is used.

While it is obvious that he can perfectly read his notes using the glass, since it is designed for reading.

Since the magnifying glass is at its optimal position, the light rays coming from it to the eye will be parallel to each other. For the flora to be clearly seen, these light rays must converge at the retina.

So, the real question here is whether the focal lengths of the eye lens and the reading glass combine to get the distance from lens to retina.

The power of lens is +2 D. focal length is the inverse of power. the positive sign means that the lens is convex.

So, the focal length of the reading glass is 1/2 =0.5 m =50 cm.

the formula for addition of focal lengths is 1f=1f1+1f2

So, f=f1*f2/(f1+f2)

=50*2.6/(50+2.6) = 130/52.6=2.47cms.

Since the retina is 2.5 cm away from the screen and the image is formed 2.47cm away, Hemulens should be able to see both the flora and the notes perfectly.