Question about lenes.?

Question

How would I figure out the calculated image distance and size when using a light source and lens? I am given the object distance and size and by using a graphical approach, I have the measured image distance and size.
Would this be correct: 1/distance of object + 1/distance of image= 1/focal point
I'm just not getting this because I get fractions and I was told to find the reciprocal. The numbers I get just doesn't make much sense.

Answer 1

> 1/distance of object + 1/distance of image= 1/focal point

That is correct.

> I'm just not getting this because I get fractions and I was told to find the reciprocal. The numbers I get just doesn't make much sense.

Let's try an example.

Say the distance of the object is 30 inches, and the focal length is 10 inches. The formula says:

1/(30 inches) + 1/Di = 1/(10 inches)

("Di" = "distance of image")

Use algebra to solve for Di:

1. Subract 1/(30 in) from both sides:
1/Di = 1/(10 in) − 1/(30 in)

2. Combine the fractions on the right side:
1/Di = 1/(10 in) − 1/(30 in)
= 3/(30 in) − 1/(30 in)
= 2/(30 in)

3. Take the reciprocal of both sides:
1/Di = 2/(30 in)
Di = (30 in) / 2

4. Simplify:
Di = 15 in.

If you were to solve for Di using just symbols ("Do" for distance of object and "f" for focal length), it would look like this:

Di = (Do)(f) / (Do − f)

That formula is good for all values of Do, Di and f, provided that Do is greater than f (if Do is NOT greater than f, you don't get a focused image). So I'm not sure what the numbers are that you're getting that "don't make sense."