(c) (i) state the three properties of an image formed by a plane mirror. (ii) a ray of light enters glass…

Explanation:

Step1: State properties of plane - mirror image

1. The image is virtual (not formed on a screen).
2. The image is of the same size as the object.
3. The image is laterally inverted (left - right reversed) and at the same distance behind the mirror as the object is in front of it.

Step2: Calculate refractive index of glass

We use Snell's law $n=\frac{\sin i}{\sin r}$, where $i$ is the angle of incidence and $r$ is the angle of refraction. Given $i = 40^{\circ}$ and $r=26^{\circ}$, so $n=\frac{\sin40^{\circ}}{\sin26^{\circ}}$. $\sin40^{\circ}\approx0.6428$ and $\sin26^{\circ}\approx0.4384$, then $n=\frac{0.6428}{0.4384}\approx1.466$.

Step3: Calculate critical angle

The formula for the critical angle $C$ is $\sin C=\frac{1}{n}$. Substituting $n = 1.466$, we get $\sin C=\frac{1}{1.466}\approx0.682$. Then $C=\sin^{- 1}(0.682)\approx43^{\circ}$.

Answer:

(i) Virtual, same - size as object, laterally inverted and at the same distance behind the mirror as the object is in front. (ii) Approximately $43^{\circ}$