Question 131: Ray Optics

Question

For the thin convex lens, the radii of curvature are at $$15 \mathrm{~cm}$$ and $$30 \mathrm{~cm}$$ respectively. The focal length the lens is $$20 \mathrm{~cm}$$. The refractive index of the material is :

Accepted Answer

To find the refractive index of the material of a thin convex lens, we can make use of the Lensmaker's Formula. The Lensmaker's formula is given by:
$$\frac{1}{f} = \left( \frac{\mu - 1}{\mu} \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$
where
$f$ is the focal length of the lens,
$\mu$ is the refractive index of the material of the lens,
$R_1$ is the radius of curvature of the first surface (convex side, positive),
$R_2$ is the radius of curvature of the second surface (concave side, negative for convex lens).
Given in the question, the radii of curvature are $15 \, \mathrm{cm}$ and $30 \, \mathrm{cm}$ respectively, and the focal length $f = 20\, \mathrm{cm}$.
It's important to pay attention to the signs of the radii of curvature according to the lens maker's convention. For convex lenses, $R_1$ is positive and $R_2$ is negative; however, since the problem doesn't specify which curvature corresponds to which side in relation to the direction of light travel, we'll assume the light travels from left to right: thus, $R_1 = +15 \, \mathrm{cm}$ and $R_2 = -30 \, \mathrm{cm}$.
Substituting the given values into the Lensmaker's Formula, we get:
$$\frac{1}{20} = (\mu - 1) \left( \frac{1}{15} - \frac{1}{-30} \right) $$
$$\frac{1}{20} = (\mu - 1) \left( \frac{1}{15} + \frac{1}{30} \right) $$
$$\frac{1}{20} = (\mu - 1) \left( \frac{2 + 1}{30} \right) $$
$$\frac{1}{20} = (\mu - 1) \left( \frac{3}{30} \right) $$
$$\frac{1}{20} = (\mu - 1) \left( \frac{1}{10} \right) $$
$$\frac{1}{20} = \frac{\mu - 1}{10}$$
Now, solve for $\mu$:
$$\mu - 1 = \frac{10}{20} $$
$$\mu - 1 = 0.5 $$
$$\mu = 1.5$$
Hence, the refractive index of the material of the lens is
1.5
, which corresponds to
Option B
.

Answer

1.2

Answer

1.5

Answer

1.4

Answer

1.8

Ray Optics

For the thin convex lens, the radii of curvature are at $15 \mathrm{~cm} and 30 \mathrm{~cm} respectively. The focal length the lens is 20 \mathrm{~cm}$. The refractive index of the material is :

Choose the correct answer: