Q142 / 160 · TS EAMCET 2024 (11 May Shift 1) · Physics
A thin plano-convex lens of focal length 73.5 cm has a circular aperture of diameter 8.4 cm. If the refractive index of the material of the lens is $\frac{5}{3}$, then the thickness of the lens is nearly
- A2.4 cm
- B2.4 mm
- Correct answerC1.8 mm
- D1.8 cm
Solution
The radius of curvature of a plano-convex lens,
$R=\frac{r^2}{2 t}=\frac{d^2}{8 t}$ $\Rightarrow \mathrm{f}(\mathrm{M}-1)=\frac{\mathrm{d}^2}{8 \mathrm{t}}$ $\therefore$ Thickness, $\mathrm{t}=\frac{8.4 \times 8.4 \times 10}{8 \times 73.5\left(\frac{5}{3}-1\right)}=1.8 \mathrm{~mm}$
$R=\frac{r^2}{2 t}=\frac{d^2}{8 t}$ $\Rightarrow \mathrm{f}(\mathrm{M}-1)=\frac{\mathrm{d}^2}{8 \mathrm{t}}$ $\therefore$ Thickness, $\mathrm{t}=\frac{8.4 \times 8.4 \times 10}{8 \times 73.5\left(\frac{5}{3}-1\right)}=1.8 \mathrm{~mm}$
Hence, the correct answer is option: 'C'.