Question

A pair of eyeglasses is designed to allow a person with a far-point distance of 2.21 m to read a road sign at a distance of 22.1 m

Part A Find the focal length required of these glasses if they are to be worn 2.50 cm from the eyes.

f=______ m

Part B Find the focal length required of these glasses if they are to be worn 1.25 cm from the eyes.

f=______ m

Answer 1

Part A.

Using lens equation:

1/f = 1/u + 1/v

where Object distance without glasses (u') = 22.1 m

Image distance without glasses (v') = -2.21 m (-ve because image is on the same side of object)

Now when glasses are worn 2.50 cm from the eyes, then

actual object distance = u = u' - 2.50 cm = 22.1 - 0.0250 = 22.075 m

actual Image distance = v = -(v' - 2.50 cm) = -(2.21 - 0.0250) = -2.185 m

So Using these values:

1/f = 1/u + 1/v

f = u*v/(u + v)

f = 22.075*(-2.185)/(22.075 - 2.185)

f = focal length of lens = -2.425 m

Part B.

Now when glasses are worn 1.25 cm from the eyes, then

actual object distance = u = u' - 1.25 cm = 22.1 - 0.0125 = 22.0875 m

actual Image distance = v = -(v' - 1.25 cm) = -(2.21 - 0.0125) = -2.1975 m

So Using these values:

1/f = 1/u + 1/v

f = u*v/(u + v)

f = 22.0875*(-2.1975)/(22.0875 - 2.1975)

f = focal length of lens = -2.440 m

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