A farsighted person has a nearpoint of 54 cm from her eyes. She wants glasses th

Question

A farsighted person has a nearpoint of 54 cm from her eyes. She wants glasses that will let her see objects at a distance of only 25 cm from her eyes. Determine the focal length of the glasses needed if the glasses are 2 cm and 3 cm from her eyes. (Remember, a converging lens has a positive focal length and a diverging lens has a negative focal length.)

A nearsighted person has a farpoint of 491 cm from his left eye and 642 cm from his right eye. He wants contact lenses that will let him see objects at a great distance. Determine the focal length of the contact lens needed for each eye. (Remember, a converging lens has a positive focal length and a diverging lens has a negative focal length.)

1)

fleft =

cm  

2)

fright =

cm  

Explanation / Answer

Given,

Nearpoint of the farshighted person = 54 cm ; object dist. = 25 cm

Let f2 be the focal length of lens needed when glasses are 2 cm from the eyes. Then

object dist = o2 = 25 - 2 = 23 cm

image dist. = i2 = 54 - 2 = 52 cm

we know that,

1/f = 1/i + 1/o so f = o x i / (o + i) In this case:

f2 = o2 x i2 / (o2 + i2)

f2 = (23)(-52) / 23 + (-52) = 1196/23 =41.24 cm

Hence f2 = 41.24 cm

Now let f3 be the focal legth when lens is 3 cm apart, so i3 = 51 cm and o3 = 22cm

similarly we have

o3 = 25 - 3 = 22 cm ; i3 = 54 - 3 = 51cm

f3 = (-51) x (22 )/ (-51 + 22) = 1122/29 = 38.69 cm

hence f3 = 38.68 cm

Part (2)Given

farpoint of nearsighted person = 491 cm(left) and 642(right)

the image will be formed at infinity for both the eyes.

so we have

For left eye, we have

1/f(left) = 1/infinity - 1/491

f (left) = -491 cm

For right eye,

1/f(right) = 1/infinity - 1/642

f(right) = - 642 cm

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