Answer:
Explanation:
The lens equation is
1 / f = 1 / di + 1 / do
Where
f is focal length
di is the image distance
do is the object distance
Both Annie and Billy use a glass whose near point is 25cm
Then, the object distance is
do = 25 - 2 = 23cm
The have the same object distance.
Let find the vocal length of bills eye
Given that,
Bill near point is 121cm and distance of the glass from the eye is 2cm
Then,
Image distance of bill is
di_B = -(121-2) = -119cm
object distance do = 23cm
Then,
1 / f_B = 1 / di_B + 1 / do
1 / f_B = -1 / 119 + 1 / 23
1 / f_B = -119^-1 + 23^-1
1 / f_B = 0.0351
Then, f_B = 28.51 cm
Also, let find Annie focal length
Given that,
Annie near point is 74 cm and distance of the glass from the eye is 2cm
Then,
Image distance of Annie is
di_A = -(74-2) = -72cm
object distance do = 23cm
Then,
1 / f_A = 1 / di_A + 1 / do
1 / f_A = -1 / 72 + 1 / 23
1 / f_A = -72^-1 + 23^-1
1 / f_A = 0.02959
Then, f_A = 33.8 cm
Distance of object from the lens when Annie uses Billy glass
Then,
1 / f_B = 1 / di_A + 1 / do
1 / 28.51 = -1 / 72 + 1 / do
28.51^-1 = -72^-1 + do^-1
do^-1 = 28.51^-1 + 72^-1
do^-1 = 0.048964
do = 20.42 cm
Then, the object location from the eye will be, the eye is 2cm from the glass. Then,
do_A = 20.42 + 2 = 22.42cm
do_A = 22.42 cm
Distance of object from the lens when Billy uses Annie glass
Then,
1 / f_A = 1 / di_B + 1 / do
1 / 33.8 = -1 / 119 + 1 / do
33.8^-1 = -119^-1 + do^-1
do^-1 = 33.8^-1 + 119^-1
do^-1 = 0.03799
do = 26.32 cm
Then, the object location from the eye will be, the eye is 2cm from the glass. Then,
do_B = 26.32 + 2 = 28.32 cm
do_B = 28.32 cm
