A ray meets a glass slab of thickness 3.0 cm and refractive index 1.50 at an angle of incidence of…

Step 1. The angle of refraction. $\sin r = \dfrac{\sin 45^\circ}{1.50} = \dfrac{0.7071}{1.50}$ $= 0.4714$, so $r = 28.1^\circ$.

Step 2. The lateral shift. $d = \dfrac{t\sin(i - r)}{\cos r}$ $= \dfrac{3.0\ \text{cm} \times \sin 16.9^\circ}{\cos 28.1^\circ}$ $= \dfrac{3.0 \times 0.2902}{0.8819}\ \text{cm} = 0.987$ cm.

Step 3. The apparent depth. $\dfrac{\text{real depth}}{n} = \dfrac{3.0\ \text{cm}}{1.50} = 2.00$ cm.