Basic Farsightedness multistep question

[zimo]

Homework Statement

A man who is farsighted and standing in front of a flat mirror without glasses at some distance to see his image in focus. When he puts on his glasses he comes closer for seeing himself in focus to a distance that is 6 times shorter of the previous distance.
a. what is the shortest distance he can see without glasses?
b. what is his Diopters
c. when he puts on his wife's glasses over his he can see from 20cm distance, what kind of a sight does she have?

Homework Equations

guessing
1/f=D
1/f = 1/u + 1/v

The Attempt at a Solution

a.

with glasses he should see from a correct 25cm exactly, because of the mirror the distance is cut by half so 12.5cm distance from mirror
because the distance is 6 times more without glasses - his distance is 75 and viewing distance of 150cm
b.
to put an object in 25cm into virtual image at (-)150cm results in D=3.993
c.
object in 20cm needs to get to (-)25cm so with a second lens should put 25 into (-)150cm
with that in mind : 1/20 + 1/(-25) = 0.01 so her diopter is 0.01 [m^-1] so I'm guessing she is farsighted... (??)


I will be happy for you to review my answer and feedback either on method and results. Thanks.

 

[anathema]

Thank you for your post. Here is my response to your questions:

a. The shortest distance he can see without glasses can be calculated using the formula 1/f = 1/u + 1/v, where f is the focal length of the lens, u is the object distance, and v is the image distance. In this case, the object distance is the distance from the man's eyes to the mirror, and the image distance is the distance from the mirror to the man's eyes. Since the man is farsighted, his glasses will have a positive power, which means that they will converge light rays and bring the image closer to his eyes. Therefore, the shortest distance he can see without glasses can be calculated as follows:

1/f = 1/u + 1/v

1/f = 1/(d/2) + 1/(d/2) = 2/d

f = d/2

where d is the distance between the man's eyes and the mirror.

With glasses, the man can see at a distance of 6 times shorter than without glasses. Therefore, the new distance between the man's eyes and the mirror is d/6. Plugging this value into the equation for focal length, we get:

f = (d/6)/2 = d/12

Therefore, the shortest distance the man can see without glasses is 12 times the distance between his eyes and the mirror.

b. The man's Diopters can be calculated using the formula D = 1/f, where D is the power of the lens in Diopters and f is the focal length of the lens in meters. In this case, the man's glasses have a focal length of d/12, where d is the distance between his eyes and the mirror. Therefore, the man's Diopters can be calculated as follows:

D = 1/f = 1/(d/12) = 12/d

c. When the man puts on his wife's glasses over his own, he can see from a distance of 20cm. This means that the focal length of his wife's glasses must be -20cm. Using the formula 1/f = 1/u + 1/v, we can calculate the focal length of the combination of his glasses and his wife's glasses:

1/f = 1/u + 1/v

1/f = 1/(d/12) +