A farsighted person has a nearpoint of 56 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.)

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A patient can't see objects closer than 32 cm and wishes to clearlysee objects that are20.4 cm from his eye.

(a) Is the patient nearsighted or farsighted?

farsighted nearsighted

(b) If the eye-lens distance is 1.92cm, what is the minimum objectdistance p from thelens?
2 cm

(c) What image position with respect to the lens will allowthepatient to see the object?
3 cm

(d) Is the image real or virtual? Is theimage distance qpositive or negative?

realimage distance is negative distanceis positive virtual image

(e) Calculate the required focal length.
5 cm

(f) Find the power of the lens in diopters.
6 diopters

(g) If a contact lens is to be prescribed instead, findp,q, and f, and the power of thelens.

p	=	7 cm
q	=	8 cm
f	=	9 cm
P	=	10 diopters

A 4.0 cm tall object is 50 cm in front of a converging lens that has a 25 cm focal length.

a) Calculate the image position.

b) Calculate the image height. Type a positive value if the image is upright and a negative value if it is inverted.

lemonbutterfly300

Background information
A person with normal vision can focus on objects as close as a fewcentimeters from the eye up to objects infinitely far away. Thereexist, however, certain conditions under which the range of visionis not so extended. For example, a nearsighted person cannot focuson objects farther than a certain point (the far point), while afarsighted person cannot focus on objects closer than a certainpoint (the near point). Note that even though the presence of anear point is common to everyone, a farsighted person has a nearpoint that is much farther from the eye than the near point of aperson with normal vision.

Both nearsightedness and farsightedness can be corrected with theuse of glasses or contact lenses. In this case, the eye convergesthe light coming from the image formed by the corrective lensrather than from the object itself.

Part A
When glasses (or contact lenses) are used to correctnearsightedness, where should the corrective lens form an image ofan object located at infinity in order for the eye to form a clearimage of that object?

The lens should form the image at the far point.

Correct
PArt B If a nearsighted person has a far point d_f thatis 3.50 m from the eye, what is the focal length f₁ thecontact lenses that the person would need to see an object atinfinity clearly?

f₁ = ? m

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