MATH QUESTION
1. How far the focal length of the cornea lens system of the eye must change, when the object is moved from infinity to the near point at 10cm?
If the object is at infinity, it will give a focal length for the cornea lens system of 1.5cm, because the rays are parallel from the object and then focused by the retina.
by using the formula: 1/s +1/s'=1/f we can calculate the related to the object distance.
given: object = 25cm
image distance = 1.5cm
Let focal length = f
Then 1/25cm + 1/1.5cm = 1/f
1/f = 10/25cm + 1/15cm = 7/15cm
f = 15cm/7 = 2.14cm
So, the focal length decrease by 0.36cm
If you want to know the Diopters (the power is given in reciprocal meters)
The formula is P= 1/f diopters
P= 1/2.14cm = 47 diopters.
2. The question from the textbook of Physics: If the near point of your
eye is 75cm. What power reading glasses you need to bring your near
point to 25cm?
From the picture, we can understand that object is 25cm from a converging lens, erect image at s'=75cm.
given s = 25cm and s'= -75cm
1/25cm + 1/ -75cm = 1/f
1/f = 2/75cm = 1/0.375 = 2.67diopters
f= 1/2.67m-1 = 0.375=37.5cm
so, the reading glasses is 2.67 diopters and the focal length of the glasses is 37.5cm
Understand The Image
The image on the retina is small because the height y is far object from the eye.
When the same object is closer to eye, the image on the retina is larger.
The angle subtended is theta = y'/1.5cm
which y' = 1.5cm theta = 1.5cm y/s