The refractive index of a material of a plano | vedclass

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(A) For a plano-concave lens,one surface is plane $(R_1 = \infty)$ and the other is concave $(R_2 = 0.3 ~m)$. According to the sign convention,for a c

Vedclass · Accepted Answer

$-0.45$

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(A) For a plano-concave lens,one surface is plane $(R_1 = \infty)$ and the other is concave $(R_2 = 0.3 ~m)$. According to the sign convention,for a concave surface,$R_2 = +0.3 ~m$ (if light enters from the plane side) or $R_1 = -0.3 ~m$ (if light enters from the curved side). Using the Lens Maker's formula: $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} ight)$. For a plano-concave lens,$R_1 = \infty$ and $R_2 = 0.3 ~m$. Substituting the values: $\frac{1}{f} = (\frac{5}{3} - 1) \left( \frac{1}{\infty} - \frac{1}{0.3} ight)$. $\frac{1}{f} = (\frac{2}{3}) 	imes (0 - \frac{1}{0.3}) = -\frac{2}{3 	imes 0.3} = -\frac{2}{0.9} = -\frac{20}{9}$. $f = -\frac{9}{20} ~m = -0.45 ~m$.

The refractive index of a material of a plano-concave lens is $5/3$,and the radius of curvature is $0.3 ~m$. The focal length of the lens in air is (in $~m$)

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