A narrow beam of light is incident on thick plano convex lens of refractive index $\frac{3}{2}$ and thickness 5 cm as shown in figure. Radius of curved surface is R = 10 cm, then distance of point where beam converges from B is n cm, here n is (Round upto two digits after the decimal point.)

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Solution

By $\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\frac{3}{2 V_{A}} - \frac{1}{\infty} = \frac{3}{2} - \frac{1}{10} \Rightarrow V_{A} = 30 c m$

By $\frac{2}{3} = \frac{sin i}{sin r} = \frac{tan i}{tan r}$

$\Rightarrow \frac{2}{3} = \frac{V_{B}}{25} \Rightarrow V_{B} = \frac{50}{3} = 16.67$ cm

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