Question

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$,

Answer 1

$v=\frac{40}{3}$

Answer 2

We use the lens formula:

$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

For a convex lens $u$ is taken as $-40$ (object on the left) and $f=10$. Plug in the values:

$$\frac{1}{v} - \left(-\frac{1}{40}\right) = \frac{1}{10} \quad \Rightarrow \quad \frac{1}{v} + \frac{1}{40} = \frac{1}{10}$$

Subtract $\frac{1}{40}$ from both sides:

$$\frac{1}{v} = \frac{1}{10} - \frac{1}{40} = \frac{4-1}{40} = \frac{3}{40}$$

Thus,

$$v = \frac{40}{3}$$

Explanation:

1. Use the formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.
2. Substitute $u=-40$ and $f=10$.
3. Solve: $\frac{1}{v} = \frac{3}{40}$ so $v=\frac{40}{3}$.