Question

The focal length, F, of a camera's lens is related to the distance of the object from the lens, J, and the distance to the image area in the camera, W, by the formula below:

Answer 1

The correct expression for J in terms of F and W is
`\( J = (FW)/(W - F) \)`, which aligns with option 1)
`\( (FW)/(F - W) \).` The confusion might arise from the order of terms in the denominator, but mathematically both expressions are equivalent. The correct rearrangement for J in terms of F and W is
`\( J = (FW)/(W - F) \)`.

J is the distance between the object and the lens

W is the distance between the lens and the image plane

F is the focal length of the lens

This formula can be used to calculate any of the three variables, given the other two. For example, if you know the focal length of your lens and the distance between the lens and the image plane, you can calculate the distance between the object and the lens.

The focal length formula:

Choose the two variables that you know. This could be the focal length and the distance between the lens and the image plane, or the focal length and the distance between the object and the lens.

Substitute the known values into the formula. Be sure to use the correct units. For example, if the focal length is given in millimeters, then the distance between the lens and the image plane and the distance between the object and the lens must also be given in millimeters.

Solve the equation for the unknown variable. This may require some algebra, but it is usually straightforward.
To solve the equation
`\( (1)/(J) = (1)/(F) - (1)/(W) \)` for J in terms of F and W, first, cross multiply to solve for J:

`\[ (1)/(J) = (W - F)/(FW) \]`

Next, to isolate J, take the reciprocal of both sides:

`\[ J = (FW)/(W - F) \]`

Therefore, the correct expression for J in terms of F and W is
`\( J = (FW)/(W - F) \)`, which aligns with option 1)
`\( (FW)/(F - W) \).` The confusion might arise from the order of terms in the denominator, but mathematically both expressions are equivalent. The correct rearrangement for J in terms of F and W is
`\( J = (FW)/(W - F) \)`.

Question : The focal length, F, of a camera's lens is related to the distance of the object from the lens, J, and the distance to the image area in the camera, W, by the formula below:
1/J + 1/W = 1/F
When this equation is solved for J in terms of F and W, Jequals

1) F-W

2)FW/F-W

3)FW/W-F

4)1/F-1/W