Question from simple lens diagram (camera)

ZedCar

1. The problem statement, all variables and given/known data
A simple camera has a converging lens of focal length 50.0 mm.

It is used to photograph a tree 3.00 m high.

The tree is 8.00 m away from the lens.

Calculate the distance v between the lens and the film, giving your answer in mm to three significant figures.


2. Relevant equations

1/f = 1/u + 1/v

3. The attempt at a solution

1/50 = 1/8000 + 1/(-v)
v = -50.3 mm

Is this correct? Thank you!

Squeezebox

Why did you reason that the image distance was negative?

ZedCar

Hmmm, not sure why I done that actually...

Have corrected to:

1/f = 1/u + 1/v

1/50 = 1/8000 + 1/v

v = 50.3 mm

Squeezebox

That looks right. The negative image distance you got before implies that the film needed to be outside the camera to capture the image.

ZedCar

Thanks Squeezebox!

When I want to calculate the linear magnification of the image, the following equation is used:

m = v/u

Do I use the same v and u values from above? (both in metres)

i.e.

0.0503 / 8 = 0.0063

Squeezebox

Now you have the opposite problem. There's a negative sign in this one.

m= -v/u

The image gets flipped upside down. This happens with your eyes too; your brain flips the image back right side up.

ZedCar

Ah, so it'd be

-0.0503 / 8 = -0.0063

So is the height of the tree, stated in the question as being 3.00 m, not required to obtain the linear magnification?