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  • The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is . The focal lengt

The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 \times 10^{8}ms^{-1}. The focal length of the lens is ________.
 
Option: 1 0.30 cm
Option: 2 1.5 cm
Option: 3 15 cm  
Option: 4 30 cm

Answers (1)

best_answer

\begin{array}{l} R^{2}=d^{2}+(R-t)^{2} \\ R^{2}-d^{2}=R^{2}\left\{1-\frac{t}{R}\right\}^{2} \\ 1-\frac{d^{2}}{R^{2}}=1-\frac{2 t}{R} \\ R=\frac{(3)^{2}}{2 \times(0.3)}=\frac{90}{6}=15 \mathrm{~cm} \end{array}

\begin{array}{l} \frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \\ \\ \frac{1}{f}=\left(\frac{3}{2}-1\right)\left(\frac{1}{15}\right) \\ \\ f=30 \mathrm{~cm} \end{array}

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