The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is

<p>To determine the refractive index ($\mu$) of a thin convex lens, we use the lens maker's formula:</p> <p>$ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $</p> <p>Given:</p> <p><p>Focal length ($f$) = 12 cm</p></p> <p><p>Radii of curvature ($R_1$ and $R_2$) = 10 cm and -15 cm, respectively</p></p> <p>Substituting these values into the formula, we have:</p> <p>$ \frac{1}{12} = (\mu - 1) \left( \frac{1}{10} - \frac{1}{-15} \right) $</p> <p>Simplifying the equation:</p> <p>$ \frac{1}{12} = (\mu - 1) \left( \frac{3 + 2}{30} \right) $</p> <p>$ \frac{1}{12} = (\mu - 1) \times \frac{5}{30} $</p> <p>$ \frac{1}{12} = (\mu - 1) \times \frac{1}{6} $</p> <p>Solving for $\mu$:</p> <p>$ \mu - 1 = \frac{1}{12} \times 6 $</p> <p>$ \mu - 1 = \frac{1}{2} $</p> <p>$ \mu = \frac{3}{2} $</p> <p>Thus, the refractive index of the lens material is $\mu = 1.5$.</p>