The lens-to-retina distance of a woman is 1.96 cm, and the relaxed power of her eye is 55.2 D.
a) What is her far point?
b)What eyeglass power will allow her to see distant objects clearly, if her glasses are 1.80 cm from her eyes?
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To find the answers to these questions, we will need to use the lens formula and the formula for the far point.
a) The lens formula is given by:
1/f = 1/v - 1/u
Where f is the focal length of the lens (in meters), v is the distance of the image (in meters), and u is the distance of the object (in meters).
In this case, we want to find the far point, which is the distance at which the eye can see distant objects without any accommodation. For distant objects, u is approximately infinity, so we can ignore the 1/u term in the lens formula.
Using the lens formula, we can rearrange it to solve for v:
1/v = 1/f
v = f
The relaxed power of the eye is given as 55.2 D, which is equivalent to a focal length of 1 / (55.2 * 0.01) = 0.0181 m.
So, the far point of the woman's eye is approximately 0.0181 m or 18.1 cm.
b) To find the eyeglass power that will allow her to see distant objects clearly when her glasses are 1.80 cm from her eyes, we can use the lens formula again.
In this case, we need to find the object distance (u) for clear vision with the glasses. The image distance (v) is the distance between the glasses and the eye (1.80 cm or 0.0180 m).
Using the lens formula again, we can solve for u:
1/v = 1/f - 1/u
Since the woman wants to see distant objects clearly, u can be approximated as infinity (just like for the far point).
Thus, the equation becomes:
1/v = 1/f
v = f
Using the casual power of 55.2 D (focal length of 0.0181 m), the image distance would also be 0.0181 m or 18.1 cm.
Now, we can calculate the eyeglass power by using the lens formula:
1/f_glasses = 1/v - 1/u
Since u is the distance at which the object is situated, which is the difference between the distance of the glasses from the eye (1.80 cm or 0.0180 m) and the distance of the image formed by the glasses (18.1 cm or 0.181 m), we can write:
u = v - 0.0180 m
Substituting the values into the lens formula:
1/f_glasses = 1/0.0181 - 1/(0.0181 - 0.0180)
1/f_glasses = 1/0.0181 - 1/0.0001
1/f_glasses = 55.248
The eyeglass power (1/f_glasses) is approximately 55.25 D.