Question

which shows the correct lens equation?
$\frac{1}{f}=\frac{1}{d_{i}} \times \frac{1}{d_{o}}$
$\frac{1}{f}=\frac{d_{o}}{d_{i}}+\frac{d_{i}}{d_{o}}$
$\frac{1}{f}=\frac{1}{d_{o}}-\frac{1}{d_{i}}$
$\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}$

Explanation:

Step1: Recall the lens formula

The lens formula is a fundamental equation in optics. It relates the focal length ($f$) of a lens, the object distance ($d_{o}$), and the image distance ($d_{i}$).

Step2: Analyze each option

• For the first option $\frac{1}{f}=\frac{1}{d_{i}}\times\frac{1}{d_{o}}$, this is not the correct form of the lens formula.
• For the second option $\frac{1}{f}=\frac{d_{o}}{d_{i}}+\frac{d_{i}}{d_{o}}$, this is also not the correct form.
• For the third option $\frac{1}{f}=\frac{1}{d_{o}}-\frac{1}{d_{i}}$, this is incorrect.
• For the fourth option $\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}$, this is the well - known and correct lens formula.

Answer:

$\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}$ (the fourth option)