Question

The lens formula is given by :
\[\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\]
Which of the following correctly identifies each term in the formula?

• A. f = focal length, v = object distance, u = image distance
• B. f = focal length, v = image distance, u = object distance
• C. f = image distance, v = object distance, u = focal length
• D. f = object distance, v = focal length, u = image distance

Hint:

To avoid confusion between the lens and mirror formulas:
- Mirror formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
- Lens formula: \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\)
In both formulas, \(v\) is the image distance and \(u\) is the object distance.

Answer 1

The Correct Option is B

Step 1: Look at what each letter is measuring.
In any lens problem we always need three distances or lengths, one that is a fixed property of the lens itself, one for where the object sits, and one for where the image forms.
Step 2: Match $f$ to the lens property.
$f$ does not change when we move the object around, it is fixed for a given lens, so it stands for the focal length.
Step 3: Match $u$ and $v$ using where they are measured from.
By convention, $u$ is measured to the object before refraction happens, so it is the object distance, and $v$ is measured to where the image actually forms after refraction, so it is the image distance.
Step 4: Confirm against the formula. \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] with $f$ = focal length, $v$ = image distance, $u$ = object distance is exactly the standard convention.
\[ \boxed{f = \text{focal length},\ v = \text{image distance},\ u = \text{object distance}} \]