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

$A$ thin plano-convex lens of focal length $73.5 \ cm$ has a circular aperture of diameter $8.4 \ cm$. If the refractive index of the material of the lens is $\frac{5}{3}$, then the thickness of the lens is nearly

The focal length of a lens is $10 \ cm$. What is the power of the lens in dioptre (in $D$)?

In the displacement method of a lens,we obtain two images for different positions of the lens. One image is magnified,and the other is diminished. If $m$ is the magnification of the first image,then the focal length of the lens is given by:

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a concave lens of focal length $16 \, cm$ (in $, cm$)?

Explain the first focal centre (first principal focus) and second focal centre (second principal focus) for a biconvex lens and a biconcave lens with the help of diagrams.

Vedclass Test Series

Exam Paper Generator

Online Exam Module