(a) Monochromatic light of frequency 5.0 × 10^14 Hz passes from air into a medium of refractive index 1 · 5. Find the wavelength of the light (i)…

(i) \[\begin{aligned} & v=v \lambda \\ & 3 \times 10^{8}=5 \times 10^{14} \times \lambda \\ & \lambda=600 \mathrm{~nm} \text { or } 6 \times 10^{-7} \mathrm{~m} \end{aligned} \]

(ii) \[\begin{aligned} \lambda_{\text {medium }} & =\frac{\lambda_{\text {air }}}{\mu} \\ \lambda_{\text {medium }} & =\frac{600 \mathrm{~nm}}{1.5} \\ & =400 \mathrm{~nm} \text { or } 4 \times 10^{-7} \mathrm{~m} \end{aligned} \]

(b) \[\begin{aligned} & \frac{1}{f}=(\mu-1)\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right) \\ & \frac{1}{16}=(1.4-1)\left(\frac{1}{\mathrm{R}}-\frac{1}{\infty}\right) \\ & \frac{1}{16}=0.4 \times \frac{1}{\mathrm{R}} \\ & \mathrm{R}=16 \times 0.4 \\ & \mathrm{R}=6.4 \mathrm{~cm} \end{aligned} \]