Question

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker’s formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification.

The radii of curvature of two surfaces of a convex lens are R and 2R. If the focal length of this lens is ${\displaystyle \left(\frac{4}{3}\right)R}$, the refractive index of the material of the lens is ______.

विकल्प

• ${\displaystyle \frac{5}{3}}$

• ${\displaystyle \frac{4}{3}}$

• ${\displaystyle \frac{3}{2}}$

• ${\displaystyle \frac{7}{5}}$

Answer 1

The radii of curvature of two surfaces of a convex lens are R and 2R. If the focal length of this lens is ${\displaystyle \left(\frac{4}{3}\right)R}$, the refractive index of the material of the lens is ${\displaystyle \underline{\frac{3}{2}}}$.

Explanation:

${\displaystyle \frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})}$

⇒ ${\displaystyle \frac{3}{4R}=(\mu -1)(\frac{1}{R}+\frac{1}{2R})}$

⇒ ${\displaystyle \frac{3}{4R}=(\mu -1)\left(\frac{3}{2R}\right)}$

⇒ ${\displaystyle \mu -1=\frac{1}{2}}$

⇒ ${\displaystyle \mu =\frac{3}{2}}$