A reflective spherical balloon

[lorenz0]

Homework Statement

A balloon has a fully reflective spherical surface with a diameter of $8 cm$.
Determine the distance of an object whose reflected image appears to be reduced to $3/4$ of its real size.
Is the image upright or inverted?

Relevant Equations

$\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$, $f=-\frac{R}{2}$, $M=-\frac{q}{p}$

From ray tracing I would say that the image is upright.
Using the equation $\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$ with $f=-\frac{R}{2}=-2$ and $M=-\frac{q}{p}=\frac{3}{4}$ I get $p=\frac{2}{3}cm\simeq 0.67 cm$.

Is this correct? Thanks

 

[Charles Link]

It looks correct to me.