Question 102: Ray Optics

Question

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

Accepted Answer

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

Answer

1.4

Answer

1.8

Answer

1.5

Answer

1.2

Ray Optics

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

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