A ray of light travelling through rarer medium is incident at a very small angle 'i' on a glass slab and after refraction its velocity is reduced by $20 \%$. The angle of deviation is

Let the velocity of light in air be $v_1$ and in glass be $v_2$, with corresponding refractive indices $n_1 = 1$ and $n_2$. The velocity decreases by 20%, so $v_2 = 0.8v_1$.

Using the relation $n \propto 1/v$, we have $\frac{n_1}{n_2} = \frac{v_2}{v_1} = 0.8$. Solving gives $n_2 = \frac{1}{0.8} = \frac{5}{4}$.

Snell's law states $n_1 \sin i = n_2 \sin r$. For small angles, $\sin \theta \approx \theta$, so $i = \frac{5}{4}r$ and $r = \frac{4}{5}i$.

The deviation is $\delta = i - r = i - \frac{4}{5}i = \frac{1}{5}i$.