Question

Sol. [Key Concept: Apply $\frac{\mu_{2}}{v} - \frac{\mu_{1}}{u} = \frac{\mu_{2} - \mu_{1}}{R}$, then the magnification.]

$$\frac{\mu_{2}}{v} - \frac{\mu_{1}}{\mu} = \frac{\mu_{2} - \mu_{1}}{R} $$

$$\frac{1.54}{v} - \frac{1}{( - 40)} = \frac{1.54 - 1}{- 20} $$

$$\frac{1.54}{v} = - \frac{1}{40} - \frac{0.54}{20} $$

$$\frac{1.54}{v} = \frac{- 2.08}{40} $$

$$v = - 29.61\text{ }cm $$

$$\frac{h_{i}}{h_{0}} = \frac{\mu_{1}v}{\mu_{2}u} = \frac{1( - 29.61)}{1.54( - 40)} = 0.48 $$

$$h = 0.48 \times 2 = 0.96 \approx 1\text{ }cm $$