Focal length of a convex lens will be maximum | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) According to the lens maker's formula,the focal length $f$ of a lens is given by:$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \ri

Vedclass · Accepted Answer

red light

Vedclass · Answer

(C) According to the lens maker's formula,the focal length $f$ of a lens is given by:$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$where $\mu$ is the refractive index of the lens material.From this,we can see that $\frac{1}{f} \propto (\mu - 1)$,which implies $f \propto \frac{1}{\mu - 1}$.According to Cauchy's dispersion formula,the refractive index $\mu$ is inversely proportional to the wavelength $\lambda$ of light $(\mu \propto \frac{1}{\lambda})$.As the wavelength $\lambda$ increases,the refractive index $\mu$ decreases.Since $f \propto \frac{1}{\mu - 1}$,a decrease in $\mu$ leads to an increase in the focal length $f$.Among the given colors,red light has the maximum wavelength $(\lambda_{red} > \lambda_{yellow} > \lambda_{green} > \lambda_{blue})$.Therefore,the refractive index $\mu$ is minimum for red light,which results in the maximum focal length for red light.

Focal length of a convex lens will be maximum for

Similar Questions

$A$ convex lens of refractive index $1.5$ and focal length $f = 18 \ cm$ is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $\alpha \times f$. The value of $\alpha$ is . . . . . . . (Refractive index of water $= 4/3$)

$A$ thin double convex lens has radii of curvature each of magnitude $40 \; cm$ and is made of glass with refractive index $1.65$. Its focal length is nearly....... $cm$.

$A$ thin convex lens of focal length $f$ made of crown glass is immersed in a liquid of refractive index $\mu_l$ $(\mu_l > \mu_c)$,where $\mu_c$ is the refractive index of the crown glass. The convex lens now acts as:

$A$ screen is placed $100 \,cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \,cm$. The focal length of the lens is (in $\,cm$)

The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is

Vedclass Test Series

Exam Paper Generator

Online Exam Module