A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ________° (in degree). (Round off to the Nearest Integer)

We have an achromatic combination of a crown glass prism and a flint glass prism that produces a net deviation of $$\delta = 2°$$ for yellow light. The given data is: dispersive power of crown glass $$\omega_c = 0.02$$, dispersive power of flint glass $$\omega_f = 0.03$$, refractive index of crown glass for yellow light $$\mu_c = 1.5$$, and refractive index of flint glass for yellow light $$\mu_f = 1.6$$.

For a thin prism, the deviation for yellow light is $$\delta = (\mu - 1)A$$, where $$A$$ is the refracting angle. So the deviations produced by the crown and flint prisms are:

$$\delta_c = (\mu_c - 1)A_c = (1.5 - 1)A_c = 0.5 A_c$$

$$\delta_f = (\mu_f - 1)A_f = (1.6 - 1)A_f = 0.6 A_f$$

For an achromatic combination, the net angular dispersion must be zero. The angular dispersion of each prism equals $$\omega \times \delta$$, where $$\omega$$ is the dispersive power. The condition for achromatism is:

$$\omega_c \delta_c + \omega_f \delta_f = 0$$

$$0.02 \times 0.5 A_c + 0.03 \times 0.6 A_f = 0$$

$$0.01 A_c + 0.018 A_f = 0$$

This gives $$A_f = -\frac{0.01}{0.018} A_c = -\frac{5}{9} A_c$$. The negative sign indicates the flint glass prism is placed in the reversed orientation relative to the crown glass prism.

The net deviation condition gives:

$$\delta_c + \delta_f = 2°$$

$$0.5 A_c + 0.6 A_f = 2$$

Substituting $$A_f = -\frac{5}{9} A_c$$:

$$0.5 A_c + 0.6 \times \left(-\frac{5}{9}\right) A_c = 2$$

$$0.5 A_c - \frac{3.0}{9} A_c = 2$$

$$0.5 A_c - \frac{1}{3} A_c = 2$$

$$\frac{3 - 2}{6} A_c = 2$$

$$\frac{1}{6} A_c = 2$$

$$A_c = 12°$$

The refracting angle for the crown glass prism is $$\boxed{12}$$°.