The slab of a material of refractive index 2 | vedclass

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(B) For refraction at a spherical surface,the formula is:$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$Here,the light travels from the

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$30$

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(B) For refraction at a spherical surface,the formula is:$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$Here,the light travels from the material $(\mu_1 = 2)$ to air $(\mu_2 = 1)$.The pole $P$ is the origin. The object $O$ is at $15 \, cm$ from $P$ inside the material,so $u = -15 \, cm$.The radius of curvature $R$ for the convex surface $APB$ (as seen from the left) is $-10 \, cm$ (using sign convention).Substituting the values:$\frac{1}{v} - \frac{2}{-15} = \frac{1 - 2}{-10}$$\frac{1}{v} + \frac{2}{15} = \frac{-1}{-10} = \frac{1}{10}$$\frac{1}{v} = \frac{1}{10} - \frac{2}{15} = \frac{3 - 4}{30} = -\frac{1}{30}$$v = -30 \, cm$.The negative sign indicates that the image $I$ is virtual and formed at a distance of $30 \, cm$ to the left of $P$.

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