A question of distance

[Roy Churchill]

Might seem a silly question but I was wondering how you would calculate the following:

If I shoot a target from 2.5 metres with a 300mm lens how near would I have to be to get the target the same size in the frame if I used a 100mm lens? (assuming a 1.6 crop camera in both cases).

Is there a simple calculation or are there other factors to consider?

[Roy Churchill]

33 views and no one has come up with an answer - I guess it must be difficult to calculate !

[David Smith]

Near as I can calculate, you would have to be .833333 meters from your subject..

Dave

[Desmond Chan]

33 views and no one has come up with an answer

Too bad not all of us are rocket scientists :D

I guess it must be difficult to calculate !

Well, since you also have to ask...;)

[Mike Milicia]

Dave is correct.

Here is some background info :

The subject size will INCREASE with the square of the focal length, i.e. doubling the focal length increases the area taken up by the subject by a factor of 4.

The subject size will DECREASE with the square of the distance, i.e. doubling the distance decreases the area taken up by the subject by a factor of 4.

Since changing the focal length or distance increases or decreases the subject size with the square of the change, this leads to the following type of relationship :

If you increase both the focal length and the distance by a factor of x, the subject size remains the same.
Likewise, if you decrease the focal length and the distance by a factor of x, the subject size remains the same.

So to maintain subject size as you decrease focal length by factor of x, you would have decrease the distance by
a factor of x.
In your example, you want to decrease the focal length by a factor of 3 so you also have to decrease the distance by a factor of 3, i.e. 2.5 metres / 3 = 0.833333 metres.

The crop factor of the sensor remains constant so does not enter into the equation.

Note however that even though the subject size with the 100mm lens will take up the same area in the frame at one third the distance, you will have a wider angle of view so you will see much more of the background surrounding the subject with the shorter focal length.

[Roy Churchill]

Thank you Dave and Mike.
Mike has explained it well. Seems like The bottom line is that you decrease the distance by the same factor as the decrease in focal length - Easy when you know how :)

[Alfred Forns]

That was simple :) Thanks for the explanation !!