A camera uses a 10.5 cm focal-length converging lens to focus the image of a person onto a piece of camera exposure film.
The correct answer and explanation is:
To solve this problem, we need to understand the basic lens formula: 1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
Where:
- ff is the focal length of the lens
- dod_o is the object distance (distance from the lens to the person)
- did_i is the image distance (distance from the lens to the film or image plane)
In this case, the focal length ff is given as 10.5 cm, and it is a converging lens, so the focal length is positive.
The lens formula shows that the sum of the reciprocals of the object distance and the image distance equals the reciprocal of the focal length. By rearranging the formula, we can solve for any of the three unknowns if we are given two. Specifically, we can find the object distance dod_o or the image distance did_i if one of them is known.
Now, the image distance did_i would be the distance between the lens and the film, which is important to know to set the camera correctly. If the object distance is known, you can use the formula to calculate the exact position where the film should be placed to get a sharp image.
Example Calculation:
Suppose the object (the person) is 100 cm away from the lens. We can calculate the image distance using the lens formula: 110.5=1100+1di\frac{1}{10.5} = \frac{1}{100} + \frac{1}{d_i}
Solving for did_i, you get the image distance. This helps the photographer place the film at the correct distance to achieve a focused image.
In summary, the camera uses the lens to form a sharp image of the person on the film by adjusting the position of the film based on the image distance calculated using the lens formula.