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 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.

A thin converging lens of focal length $\displaystyle 20$ cm and a thin diverging lens of focal length $\displaystyle 15$ cm are placed coaxially in contact. The power of the combination is

$\displaystyle \frac{-5}{6} \mathrm{D}$

$\displaystyle \frac{-5}{3} \mathrm{D}$

$\displaystyle \frac{4}{3} \mathrm{D}$

$\displaystyle \frac{3}{2} \mathrm{D}$

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

$\displaystyle \frac{5}{3}$

$\displaystyle \frac{4}{3}$

$\displaystyle \frac{3}{2}$

$\displaystyle \frac{7}{5}$

The focal length of an equiconvex lens

increases when the lens is dipped in water.

increases when the wavelength of incident light decreases.

increases with decrease in radius of curvature of its surface.

decreases when the lens is cut into two identical parts along its principal axis.

A thin convex lens L of focal length $\displaystyle 10$ cm and a concave mirror M of focal length $\displaystyle 15$ cm are placed coaxially $\displaystyle 40$ cm apart as shown in figure. A beam of light coming parallel to the principal axis is incident on the lens. The final image will be formed at a distance of