\begin{tabular}{l} A diverging'lens can form a real image. \ True \ False \ Question 21 \ Whaby lionturtle sits 50 cm from a converging lens. It's image appears at -80 cm . \ What is the lens's focal length? \ \hline\end{tabular}

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Let's break down the problem step by step.

### Known Conditions:
1. The lens is a converging lens.
2. The object distance $$ d_o = 50 \, \text{cm} $$ (positive because it's on the same side as the incoming light).
3. The image distance $$ d_i = -80 \, \text{cm} $$ (negative because it's a virtual image formed on the opposite side of the lens).

### Lens Formula:
The lens formula relates the object distance, image distance, and focal length $$ f $$ of a lens:
$$
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
$$

### Step 1: Substitute the known values into the lens formula.
We will substitute $$ d_o = 50 $$ and $$ d_i = -80 $$ into the lens formula.

### Step 2: Calculate the focal length $$ f $$.
Let's perform the calculation:
$$
\frac{1}{f} = \frac{1}{50} + \frac{1}{-80}
$$

Now, we will calculate this expression.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{50}+\frac{1}{\left(-80\right)}$$
- step1: Remove the parentheses:
  $$\frac{1}{50}+\frac{1}{-80}$$
- step2: Rewrite the fraction:
  $$\frac{1}{50}-\frac{1}{80}$$
- step3: Reduce fractions to a common denominator:
  $$\frac{8}{50\times 8}-\frac{5}{80\times 5}$$
- step4: Multiply the numbers:
  $$\frac{8}{400}-\frac{5}{80\times 5}$$
- step5: Multiply the numbers:
  $$\frac{8}{400}-\frac{5}{400}$$
- step6: Transform the expression:
  $$\frac{8-5}{400}$$
- step7: Subtract the numbers:
  $$\frac{3}{400}$$
Calculate or simplify the expression $$ 1/(3/400) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{\frac{3}{400}}$$
- step1: Multiply by the reciprocal:
  $$\frac{400}{3}$$
### Step 3: Calculate the focal length $$ f $$

From the previous calculation, we found:
$$
\frac{1}{f} = \frac{3}{400}
$$

To find $$ f $$, we take the reciprocal:
$$
f = \frac{400}{3} \approx 133.33 \, \text{cm}
$$

### Conclusion:
The focal length of the converging lens is approximately $$ 133.33 \, \text{cm} $$.

### Additional Note:
Regarding the first statement about a diverging lens forming a real image, the answer is **False**. A diverging lens cannot form a real image; it only forms virtual images.
The lens's focal length is approximately 133.33 cm.

\begin{tabular}{l} A diverging'lens can form a real image. \\ True \\ False \\ Question 21 \\ Whaby lionturtle sits 50 cm from a converging lens. It's image appears at -80 cm . \\ What is the lens's focal length? \\ \hline\end{tabular}

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