If a nearsighted person can only see clearly out to 80 cm, what focal length gla

Question

If a nearsighted person can only see clearly out to 80 cm, what focal length glasses should they wear in order to see clearly objects that are far away? Assume the lenses are 2 cm from the eye. A farsighted person has a near point of 125 cm. What focal length contact lenses should this person wear in order to see clearly objects as close as 25 cm away? Of course the contacts are at the eye's location. A convex parabolic mirror has a focal length of -18 cm. If an object is placed 18 cm to the left of the convex mirror on its optical axis A) Where is the image? Is it real or virtual? B) What is the magnification of the image? c) Sketch the ray diagram for the object, mirror and image.

Explanation / Answer

7) a) the image formed is 9cm behind the mirror (to the right of convex mirror). Image formed is virtual and erect.

Using mirror formula: 1/f = 1/v+1/u

1/18 = 1/v - 1/18

1/v = 2/18

v = 9cm

b) Magnification of the image, m = - v/u = - 9/-18 = 1/2

5)

Remember a diverging lens is required to correct near sightedness. That is, the focal length of the lens is negative.

d0 =

1/d0 = 0

1/f = 1/d0 + 1/di =1/di

di = fi = -80cm = -.8m

di is negative so f is negative and the lens must be concave or diverging.

Glasses are generally worn 2 cm in front of the eye. So, f=78 cm

6)

Remember a converging lens is required to correct far sightedness. That is, the focal length of the lens is positive. Far sighted-objects close up are blurred. Distant objects need to be imaged at most 125 cm from the eye.

d0 = 25cm , di = -125cm

f = d0di / d0+di = 25*-125 / 25-125 = +31.25cm

focal length positive implies converging lens

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