If the focal length of a double convex lens f | 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 $f$ is given by $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.This

Vedclass · Accepted Answer

Less than $f_R$

Vedclass · Answer

(C) According to the Lens Maker's Formula,the focal length $f$ is given by $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.This implies $f \propto \frac{1}{\mu - 1}$.According to Cauchy's dispersion formula,the refractive index $\mu$ is inversely proportional to the wavelength $\lambda$ $(\mu \propto \frac{1}{\lambda})$.Since the wavelength of violet light $(\lambda_V)$ is less than the wavelength of red light $(\lambda_R)$,the refractive index for violet light $(\mu_V)$ is greater than the refractive index for red light $(\mu_R)$.As $\mu_V > \mu_R$,it follows that $(\mu_V - 1) > (\mu_R - 1)$.Since $f$ is inversely proportional to $(\mu - 1)$,a larger refractive index results in a smaller focal length.Therefore,the focal length for violet light $(f_V)$ is less than the focal length for red light $(f_R)$.

If the focal length of a double convex lens for red light is $f_R$,what is its focal length for violet light?

Similar Questions

When a parallel beam of white light is incident on a converging lens,the colour which is brought to focus nearest to the lens is

$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $^a{\mu _g}$ and $^a{\mu _l}$ respectively,then

The distance $v$ of the real image formed by a convex lens is measured for various object distances $u$. $A$ graph is plotted between $v$ and $u$. Which one of the following graphs is correct?

$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens material. Then its focal length will

An object is placed on the axis of a convex lens. Its image is formed $80 \, cm$ from the object. The magnification is $3$. The focal length of the lens is.....$cm$

Vedclass Test Series

Exam Paper Generator

Online Exam Module