Question 19: Ray Optics

Question

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is $\_\_\_\_$ .

Accepted Answer

For a thin convex lens, the lens makerÃ¢ÂÂs formula is
$$ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) $$
Here, the lens has the same radius of curvature on both sides, so let each radius be $R$.
For a biconvex lens:
$$ R_1 = +R,\qquad R_2 = -R $$
So,
$$ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R} - \frac{1}{-R}\right) $$
$$ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R} + \frac{1}{R}\right) $$
$$ \frac{1}{f} = (\mu - 1)\frac{2}{R} $$
Given refractive index,
$$ \mu = 1.4 $$
Then,
$$ \mu - 1 = 0.4 $$
So,
$$ \frac{1}{f} = 0.4 \cdot \frac{2}{R} = \frac{0.8}{R} $$
Hence,
$$ f = \frac{R}{0.8} = 1.25R $$
Therefore,
$$ \frac{f}{R} = 1.25 $$
So the correct option is:
$$ \boxed{1.25} $$
Option D.

Answer

0.5

Answer

2.5

Answer

0.8

Answer

1.25

Ray Optics

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is \_\_\_\_ .

Choose the correct answer: