In the diagram below, u is the object distance from a lens and v is the distance of the image produced. The slope of the graph represents the

The lens formula is given by:

where $f$ is the focal length.

Combine the terms on the right side:

Invert both sides:

Multiply by $(u+v)$:

This equation is in the form $y = mx$, where $y = uv$, $x = u+v$, and $m$ is the slope.

Comparing $uv = f(u+v)$ with $y = mx$, the slope $m$ is equal to $f$.
Therefore, the slope of the graph represents the focal length.

The correct option is C. focal length.

13. To calculate the quantity of heat released, we use the formula $Q = mc\Delta T$.

units where necessary.
Mass ($m$) = $100 \text{ g} = 0.1 \text{ kg}$
Specific heat capacity ($c$) = $460 \text{ Jkg}^{-1}\text{K}^{-1}$
Initial temperature ($T_1$) = $70 \text{ °C}$
Final temperature ($T_2$) = $20 \text{ °C}$

Since a change of $1 \text{ °C}$ is equivalent to a change of $1 \text{ K}$, $\Delta T = 50 \text{ K}$.

The correct option is A. $2.3 \times 10^3 \text{ J}$.