A camera with a 100 mm focal length lens is to be designed to focus on objects from 75 cm to 20 cm. How far must the lens move as the focus is adjusted from infinity to 75 cm?
Thank you!
To calculate the distance the lens must move as the focus is adjusted, you can use the lens formula:
1/f = 1/u + 1/v
Where:
- f is the focal length of the lens
- u is the distance of the object from the lens (initial position)
- v is the distance of the image from the lens (final position)
Given:
- f = 100 mm = 10 cm (since 1 cm = 10 mm)
- u = infinity (since the focus is adjusted from infinity)
- v = 75 cm
To find the distance the lens must move, we need to find the value of u when v = 75 cm. Rearrange the lens formula to solve for u:
1/u = 1/f - 1/v
Substituting the given values:
1/u = 1/10 - 1/75
To solve for u, we need to calculate the reciprocal of the right side:
1/u = (75 - 10) / (10 * 75)
1/u = 65 / 750
Now, take the reciprocal of both sides:
u = 750 / 65
u ≈ 11.54 cm
The lens must move from infinity to 75 cm, so the distance it must travel is:
Distance = u - v
Distance = 11.54 cm - 75 cm
Distance ≈ -63.46 cm
Therefore, to focus on objects from infinity to 75 cm, the lens must move approximately 63.46 cm closer to the object.