Answer:
i = f = 0.1 m until the lens moves towards the screen 0.1 m
Explanation:
For this exercise let's use the constructor equation
1 / f = 1 / o + 1 / i
Where f is the focal distance, or the distance to the object and "i" the distance to the image
It indicates that the focal distance is 100 mm (f = 100 mm), when an object is at infinity the image is formed at its focal length
1 / f = 1 / inf + 1 / i = 1 / i
i = f = 100 mm
At this point the screen is placed
For the shortest distance the lens has to move a little so the distance to the image is
f = 100 mm = 0.1 m
o = 6 pm = 6 10⁻¹² m
i = 100 + x
1 / f = 1 / o + 1 / 100+ x
1 /( 0.10 + x) = 1 / f - 1 / o
1 / 0.100+ x = 1/0.100 - 1/6 10-12
1 / 0.100 + x = 10 - 10¹¹ = -10¹¹
0.100 + x = -10⁻¹¹
x = -10⁻¹¹ -10⁻¹
x = -10⁻¹
x = - 0.1 m
This negative distance indicates that the lens moves towards the screen 0.1 m
