Two identical thin crown glass prisms, each with a refracting angle...

The deviation produced by a thin prism of refracting angle $A$ and refractive index $\mu$ is given by $\delta = (\mu - 1)A$.

For the two identical crown glass prisms, the total deviation for the yellow ray is:
$\delta_c = 2(\mu_y - 1)A$

For the inverted flint glass prism, the deviation is in the opposite direction. The deviation for the yellow ray is:
$\delta_f = (\mu_y' - 1)A'$

For no net deviation of the yellow ray, the total deviation must be zero, which implies:
$\delta_c = \delta_f$

Substituting the expressions for deviations, we get:
$2(\mu_y - 1)A = (\mu_y' - 1)A'$

Rearranging the terms to find the ratio $\dfrac{A'}{A}$:
$\dfrac{A'}{A} = \dfrac{2(\mu_y - 1)}{\mu_y' - 1}$