You did not watch your units, you are mixing inches and feet
Your equation should have been
1/2 = 1/di + 1/120 (I changed 10 feet to 120 in)
solve this for di and you get 2.03 inches.
Please help me I am so confused I think I am losing my mind.
The focal length f of a camera lens is 2 inches. The lens equation is 1/f=(1/di)+(l/do), where di is the distance between the lens and the film and do is the distance between the lens and the object.
The object to be photographed is 10 ft away. How far should the lens be from the film?
my work:
1 1 1
- = - + -
f di do
1 1 1
- = - + -
2 di 10
You subtract 1/10 and get 4/10=1/di. di=2.5
but supposedly the answer is 2.03. How?
1 1 1
- = - + -
f di do
if you can't tell what i mean, this is it: 1/f=(1/di)+(1/do)
Lol, trick question! Thank you!
In the given lens equation, 1/f = (1/di) + (1/do), we need to make sure that all the units are consistent to get the correct answer.
Let's take a closer look at the units involved:
- f: The focal length is given as 2 inches.
- di: The distance between the lens and the film is what we are trying to find.
- do: The distance between the lens and the object is given as 10 feet.
The issue in your calculation is the mismatched units between inches and feet. To solve this, we need to convert either the distance to inches or the focal length to feet. Let's convert the distance from feet to inches:
1 foot = 12 inches
So, 10 feet * 12 inches/foot = 120 inches.
Now, let's substitute the values into the lens equation:
1/2 = 1/di + 1/120
To solve for di, we can rearrange the equation:
1/di = 1/2 - 1/120
Next, we can subtract the two fractions:
1/di = (120 - 2)/240
Simplifying further:
1/di = 118/240
To isolate di, we take the reciprocal of both sides of the equation:
di/1 = 240/118
Divide and calculate:
di = 240/118 = 2.03 inches (rounded to two decimal places)
Therefore, the correct distance between the lens and the film (di) is approximately 2.03 inches, not 2.5 inches.